(3x+7)(5x-15)=180

Solution for (3x+7)(5x-15)=180 equation:

(3x+7)(5x-15)=180

We move all terms to the left:

(3x+7)(5x-15)-(180)=0

We multiply parentheses ..

(+15x^2-45x+35x-105)-180=0

We get rid of parentheses

15x^2-45x+35x-105-180=0

We add all the numbers together, and all the variables

15x^2-10x-285=0

a = 15; b = -10; c = -285;
Δ = b2-4ac
Δ = -102-4·15·(-285)
Δ = 17200
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:

$\sqrt{\Delta}=\sqrt{17200}=\sqrt{400*43}=\sqrt{400}*\sqrt{43}=20\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20\sqrt{43}}{2*15}=\frac{10-20\sqrt{43}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20\sqrt{43}}{2*15}=\frac{10+20\sqrt{43}}{30}
$