Solve 5*(4x-2) 3*(12-3x)=42

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{135 - 10185}{60}, x_{2} = \frac{135 + 10185}{60}

Alternative Form

x_{1} \approx 0.567987, x_{2} \approx 3.932013

Evaluate

5 (4 x - 2) \times 3 (12 - 3 x) = 42

Multiply the terms

15 (4 x - 2) (12 - 3 x) = 42

Expand the expression

More Steps

810 x - 180 x^{2} - 360 = 42

Move the expression to the left side

810 x - 180 x^{2} - 402 = 0

Rewrite in standard form

- 180 x^{2} + 810 x - 402 = 0

Multiply both sides

180 x^{2} - 810 x + 402 = 0

Substitute a= 180,b= - 810 and c= 402 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{810 \pm ( - 810 ) ^{2} - 4 \times 180 \times 402}{2 \times 180}

Simplify the expression

x = \frac{810 \pm ( - 810 ) ^{2} - 4 \times 180 \times 402}{360}

Simplify the expression

More Steps

x = \frac{810 \pm 81 0 ^{2} - 289440}{360}

Simplify the radical expression

More Steps

x = \frac{810 \pm 6 10185}{360}

Separate the equation into 2 possible cases

x = \frac{810 + 6 10185}{360} x = \frac{810 - 6 10185}{360}

Simplify the expression

More Steps

x = \frac{135 + 10185}{60} x = \frac{810 - 6 10185}{360}

Simplify the expression

More Steps

x = \frac{135 + 10185}{60} x = \frac{135 - 10185}{60}

Solution

x_{1} = \frac{135 - 10185}{60}, x_{2} = \frac{135 + 10185}{60}

Alternative Form

x_{1} \approx 0.567987, x_{2} \approx 3.932013

Show Solution