(9x+4)(16x-4)+80=180

Solution for (9x+4)(16x-4)+80=180 equation:

(9x+4)(16x-4)+80=180

We move all terms to the left:

(9x+4)(16x-4)+80-(180)=0

We add all the numbers together, and all the variables

(9x+4)(16x-4)-100=0

We multiply parentheses ..

(+144x^2-36x+64x-16)-100=0

We get rid of parentheses

144x^2-36x+64x-16-100=0

We add all the numbers together, and all the variables

144x^2+28x-116=0

a = 144; b = 28; c = -116;
Δ = b2-4ac
Δ = 282-4·144·(-116)
Δ = 67600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{67600}=260$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-260}{2*144}=\frac{-288}{288}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+260}{2*144}=\frac{232}{288}
=29/36
$