(x-17)(7x+5)=180

Solution for (x-17)(7x+5)=180 equation:

(x-17)(7x+5)=180

We move all terms to the left:

(x-17)(7x+5)-(180)=0

We multiply parentheses ..

(+7x^2+5x-119x-85)-180=0

We get rid of parentheses

7x^2+5x-119x-85-180=0

We add all the numbers together, and all the variables

7x^2-114x-265=0

a = 7; b = -114; c = -265;
Δ = b2-4ac
Δ = -1142-4·7·(-265)
Δ = 20416
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:

$\sqrt{\Delta}=\sqrt{20416}=\sqrt{64*319}=\sqrt{64}*\sqrt{319}=8\sqrt{319}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-8\sqrt{319}}{2*7}=\frac{114-8\sqrt{319}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+8\sqrt{319}}{2*7}=\frac{114+8\sqrt{319}}{14}
$