(16x+13)(-20x+23)=180

Solution for (16x+13)(-20x+23)=180 equation:

(16x+13)(-20x+23)=180

We move all terms to the left:

(16x+13)(-20x+23)-(180)=0

We multiply parentheses ..

(-320x^2+368x-260x+299)-180=0

We get rid of parentheses

-320x^2+368x-260x+299-180=0

We add all the numbers together, and all the variables

-320x^2+108x+119=0

a = -320; b = 108; c = +119;
Δ = b2-4ac
Δ = 1082-4·(-320)·119
Δ = 163984
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:

$\sqrt{\Delta}=\sqrt{163984}=\sqrt{16*10249}=\sqrt{16}*\sqrt{10249}=4\sqrt{10249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-4\sqrt{10249}}{2*-320}=\frac{-108-4\sqrt{10249}}{-640}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+4\sqrt{10249}}{2*-320}=\frac{-108+4\sqrt{10249}}{-640}
$