(x+15)(3x-17)=180

Solution for (x+15)(3x-17)=180 equation:

(x+15)(3x-17)=180

We move all terms to the left:

(x+15)(3x-17)-(180)=0

We multiply parentheses ..

(+3x^2-17x+45x-255)-180=0

We get rid of parentheses

3x^2-17x+45x-255-180=0

We add all the numbers together, and all the variables

3x^2+28x-435=0

a = 3; b = 28; c = -435;
Δ = b2-4ac
Δ = 282-4·3·(-435)
Δ = 6004
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:

$\sqrt{\Delta}=\sqrt{6004}=\sqrt{4*1501}=\sqrt{4}*\sqrt{1501}=2\sqrt{1501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{1501}}{2*3}=\frac{-28-2\sqrt{1501}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{1501}}{2*3}=\frac{-28+2\sqrt{1501}}{6}
$