Solve 3 (5x - 7) 2(9x - 11) = 4(8x - 7) - 111

Question

Solve the equation(The real numbers system)

x \in / R

Alternative Form

No real solution

Evaluate

3 (5 x - 7) \times 2 (9 x - 11) = 4 (8 x - 7) - 111

Multiply the terms

6 (5 x - 7) (9 x - 11) = 4 (8 x - 7) - 111

Expand the expression

More Steps

270 x^{2} - 708 x + 462 = 4 (8 x - 7) - 111

Expand the expression

More Steps

270 x^{2} - 708 x + 462 = 32 x - 139

Move the expression to the left side

270 x^{2} - 740 x + 601 = 0

Substitute a= 270,b= - 740 and c= 601 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{740 \pm ( - 740 ) ^{2} - 4 \times 270 \times 601}{2 \times 270}

Simplify the expression

x = \frac{740 \pm ( - 740 ) ^{2} - 4 \times 270 \times 601}{540}

Simplify the expression

More Steps

x = \frac{740 \pm 74 0 ^{2} - 649080}{540}

Solution

x \in / R

Alternative Form

No real solution

Show Solution

Solve using the quadratic formula in the complex numbers system

Solve by completing the square in the complex numbers system

Solve using the PQ formula in the complex numbers system

x_{1} = \frac{37}{27} - \frac{25370}{270} i, x_{2} = \frac{37}{27} + \frac{25370}{270} i

Alternative Form

x_{1} \approx 1. \dot{3} 7 \dot{0} - 0.589925 i, x_{2} \approx 1. \dot{3} 7 \dot{0} + 0.589925 i

Evaluate

3 (5 x - 7) \times 2 (9 x - 11) = 4 (8 x - 7) - 111

Multiply the terms

6 (5 x - 7) (9 x - 11) = 4 (8 x - 7) - 111

Expand the expression

More Steps

270 x^{2} - 708 x + 462 = 4 (8 x - 7) - 111

Expand the expression

More Steps

270 x^{2} - 708 x + 462 = 32 x - 139

Move the expression to the left side

270 x^{2} - 740 x + 601 = 0

Substitute a= 270,b= - 740 and c= 601 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{740 \pm ( - 740 ) ^{2} - 4 \times 270 \times 601}{2 \times 270}

Simplify the expression

x = \frac{740 \pm ( - 740 ) ^{2} - 4 \times 270 \times 601}{540}

Simplify the expression

More Steps

x = \frac{740 \pm 74 0 ^{2} - 649080}{540}

Simplify the radical expression

More Steps

x = \frac{740 \pm 2 25370 \times i}{540}

Separate the equation into 2 possible cases

x = \frac{740 + 2 25370 \times i}{540} x = \frac{740 - 2 25370 \times i}{540}

Simplify the expression

More Steps

x = \frac{37}{27} + \frac{25370}{270} i x = \frac{740 - 2 25370 \times i}{540}

Simplify the expression

More Steps

x = \frac{37}{27} + \frac{25370}{270} i x = \frac{37}{27} - \frac{25370}{270} i

Solution

x_{1} = \frac{37}{27} - \frac{25370}{270} i, x_{2} = \frac{37}{27} + \frac{25370}{270} i

Alternative Form

x_{1} \approx 1. \dot{3} 7 \dot{0} - 0.589925 i, x_{2} \approx 1. \dot{3} 7 \dot{0} + 0.589925 i

Show Solution