(9x-2)(5x+54)=180

Solution for (9x-2)(5x+54)=180 equation:

(9x-2)(5x+54)=180

We move all terms to the left:

(9x-2)(5x+54)-(180)=0

We multiply parentheses ..

(+45x^2+486x-10x-108)-180=0

We get rid of parentheses

45x^2+486x-10x-108-180=0

We add all the numbers together, and all the variables

45x^2+476x-288=0

a = 45; b = 476; c = -288;
Δ = b2-4ac
Δ = 4762-4·45·(-288)
Δ = 278416
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:

$\sqrt{\Delta}=\sqrt{278416}=\sqrt{16*17401}=\sqrt{16}*\sqrt{17401}=4\sqrt{17401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(476)-4\sqrt{17401}}{2*45}=\frac{-476-4\sqrt{17401}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(476)+4\sqrt{17401}}{2*45}=\frac{-476+4\sqrt{17401}}{90}
$