(5x+4)(8x-71)=180

Solution for (5x+4)(8x-71)=180 equation:

(5x+4)(8x-71)=180

We move all terms to the left:

(5x+4)(8x-71)-(180)=0

We multiply parentheses ..

(+40x^2-355x+32x-284)-180=0

We get rid of parentheses

40x^2-355x+32x-284-180=0

We add all the numbers together, and all the variables

40x^2-323x-464=0

a = 40; b = -323; c = -464;
Δ = b2-4ac
Δ = -3232-4·40·(-464)
Δ = 178569
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:

$\sqrt{\Delta}=\sqrt{178569}=\sqrt{9*19841}=\sqrt{9}*\sqrt{19841}=3\sqrt{19841}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-323)-3\sqrt{19841}}{2*40}=\frac{323-3\sqrt{19841}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-323)+3\sqrt{19841}}{2*40}=\frac{323+3\sqrt{19841}}{80}
$