(9x+4)(6x-4)=180

Solution for (9x+4)(6x-4)=180 equation:

(9x+4)(6x-4)=180

We move all terms to the left:

(9x+4)(6x-4)-(180)=0

We multiply parentheses ..

(+54x^2-36x+24x-16)-180=0

We get rid of parentheses

54x^2-36x+24x-16-180=0

We add all the numbers together, and all the variables

54x^2-12x-196=0

a = 54; b = -12; c = -196;
Δ = b2-4ac
Δ = -122-4·54·(-196)
Δ = 42480
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:

$\sqrt{\Delta}=\sqrt{42480}=\sqrt{144*295}=\sqrt{144}*\sqrt{295}=12\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{295}}{2*54}=\frac{12-12\sqrt{295}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{295}}{2*54}=\frac{12+12\sqrt{295}}{108}
$