Solve (5x-3) (4x 7) 61=180

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{1281 - 3 225029}{4270}, x_{2} = \frac{1281 + 3 225029}{4270}

Alternative Form

x_{1} \approx - 0.033283, x_{2} \approx 0.633283

Evaluate

(5 x - 3) (4 x \times 7) \times 61 = 180

Remove the parentheses

(5 x - 3) \times 4 x \times 7 \times 61 = 180

Multiply the terms

More Steps

1708 x (5 x - 3) = 180

Expand the expression

More Steps

8540 x^{2} - 5124 x = 180

Move the expression to the left side

8540 x^{2} - 5124 x - 180 = 0

Substitute a= 8540,b= - 5124 and c= - 180 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{5124 \pm ( - 5124 ) ^{2} - 4 \times 8540 ( - 180 )}{2 \times 8540}

Simplify the expression

x = \frac{5124 \pm ( - 5124 ) ^{2} - 4 \times 8540 ( - 180 )}{17080}

Simplify the expression

More Steps

x = \frac{5124 \pm 512 4 ^{2} + 6148800}{17080}

Simplify the radical expression

More Steps

x = \frac{5124 \pm 12 225029}{17080}

Separate the equation into 2 possible cases

x = \frac{5124 + 12 225029}{17080} x = \frac{5124 - 12 225029}{17080}

Simplify the expression

More Steps

x = \frac{1281 + 3 225029}{4270} x = \frac{5124 - 12 225029}{17080}

Simplify the expression

More Steps

x = \frac{1281 + 3 225029}{4270} x = \frac{1281 - 3 225029}{4270}

Solution

x_{1} = \frac{1281 - 3 225029}{4270}, x_{2} = \frac{1281 + 3 225029}{4270}

Alternative Form

x_{1} \approx - 0.033283, x_{2} \approx 0.633283

Show Solution