(-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^2-628x+119=0

a = 320; b = -628; c = +119;
Δ = b2-4ac
Δ = -6282-4·320·119
Δ = 242064
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{242064}=492$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-628)-492}{2*320}=\frac{136}{640}
=17/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-628)+492}{2*320}=\frac{1120}{640}
=1+3/4
$