(17x+4)(19x-2)=180

Solution for (17x+4)(19x-2)=180 equation:

(17x+4)(19x-2)=180

We move all terms to the left:

(17x+4)(19x-2)-(180)=0

We multiply parentheses ..

(+323x^2-34x+76x-8)-180=0

We get rid of parentheses

323x^2-34x+76x-8-180=0

We add all the numbers together, and all the variables

323x^2+42x-188=0

a = 323; b = 42; c = -188;
Δ = b2-4ac
Δ = 422-4·323·(-188)
Δ = 244660
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:

$\sqrt{\Delta}=\sqrt{244660}=\sqrt{4*61165}=\sqrt{4}*\sqrt{61165}=2\sqrt{61165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{61165}}{2*323}=\frac{-42-2\sqrt{61165}}{646}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{61165}}{2*323}=\frac{-42+2\sqrt{61165}}{646}
$