(x+17)(4x-17)-180=0

Solution for (x+17)(4x-17)-180=0 equation:

(x+17)(4x-17)-180=0

We multiply parentheses ..

(+4x^2-17x+68x-289)-180=0

We get rid of parentheses

4x^2-17x+68x-289-180=0

We add all the numbers together, and all the variables

4x^2+51x-469=0

a = 4; b = 51; c = -469;
Δ = b2-4ac
Δ = 512-4·4·(-469)
Δ = 10105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-\sqrt{10105}}{2*4}=\frac{-51-\sqrt{10105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+\sqrt{10105}}{2*4}=\frac{-51+\sqrt{10105}}{8}
$