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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+144x^2-36x+64x-16)-180=0

We get rid of parentheses

144x^2-36x+64x-16-180=0

We add all the numbers together, and all the variables

144x^2+28x-196=0

a = 144; b = 28; c = -196;
Δ = b2-4ac
Δ = 282-4·144·(-196)
Δ = 113680
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:

$\sqrt{\Delta}=\sqrt{113680}=\sqrt{784*145}=\sqrt{784}*\sqrt{145}=28\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28\sqrt{145}}{2*144}=\frac{-28-28\sqrt{145}}{288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28\sqrt{145}}{2*144}=\frac{-28+28\sqrt{145}}{288}
$