(5x-5)(9x+17)=180

Solution for (5x-5)(9x+17)=180 equation:

(5x-5)(9x+17)=180

We move all terms to the left:

(5x-5)(9x+17)-(180)=0

We multiply parentheses ..

(+45x^2+85x-45x-85)-180=0

We get rid of parentheses

45x^2+85x-45x-85-180=0

We add all the numbers together, and all the variables

45x^2+40x-265=0

a = 45; b = 40; c = -265;
Δ = b2-4ac
Δ = 402-4·45·(-265)
Δ = 49300
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:

$\sqrt{\Delta}=\sqrt{49300}=\sqrt{100*493}=\sqrt{100}*\sqrt{493}=10\sqrt{493}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10\sqrt{493}}{2*45}=\frac{-40-10\sqrt{493}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10\sqrt{493}}{2*45}=\frac{-40+10\sqrt{493}}{90}
$