(5x+7)(8x-71)=x

Solution for (5x+7)(8x-71)=x equation:

(5x+7)(8x-71)=x

We move all terms to the left:

(5x+7)(8x-71)-(x)=0

We add all the numbers together, and all the variables

-1x+(5x+7)(8x-71)=0

We multiply parentheses ..

(+40x^2-355x+56x-497)-1x=0

We get rid of parentheses

40x^2-355x+56x-1x-497=0

We add all the numbers together, and all the variables

40x^2-300x-497=0

a = 40; b = -300; c = -497;
Δ = b2-4ac
Δ = -3002-4·40·(-497)
Δ = 169520
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:

$\sqrt{\Delta}=\sqrt{169520}=\sqrt{16*10595}=\sqrt{16}*\sqrt{10595}=4\sqrt{10595}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-4\sqrt{10595}}{2*40}=\frac{300-4\sqrt{10595}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+4\sqrt{10595}}{2*40}=\frac{300+4\sqrt{10595}}{80}
$