x=(5x+4)(8x-71)

Solution for x=(5x+4)(8x-71) equation:

x=(5x+4)(8x-71)

We move all terms to the left:

x-((5x+4)(8x-71))=0

We multiply parentheses ..

-((+40x^2-355x+32x-284))+x=0


We calculate terms in parentheses: -((+40x^2-355x+32x-284)), so:

(+40x^2-355x+32x-284)

We get rid of parentheses

40x^2-355x+32x-284

We add all the numbers together, and all the variables

40x^2-323x-284

Back to the equation:

-(40x^2-323x-284)


We add all the numbers together, and all the variables

x-(40x^2-323x-284)=0

We get rid of parentheses

-40x^2+x+323x+284=0

We add all the numbers together, and all the variables

-40x^2+324x+284=0

a = -40; b = 324; c = +284;
Δ = b2-4ac
Δ = 3242-4·(-40)·284
Δ = 150416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{150416}=\sqrt{16*9401}=\sqrt{16}*\sqrt{9401}=4\sqrt{9401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(324)-4\sqrt{9401}}{2*-40}=\frac{-324-4\sqrt{9401}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(324)+4\sqrt{9401}}{2*-40}=\frac{-324+4\sqrt{9401}}{-80}
$