(5x+15)(6x-2)=180

Solution for (5x+15)(6x-2)=180 equation:

(5x+15)(6x-2)=180

We move all terms to the left:

(5x+15)(6x-2)-(180)=0

We multiply parentheses ..

(+30x^2-10x+90x-30)-180=0

We get rid of parentheses

30x^2-10x+90x-30-180=0

We add all the numbers together, and all the variables

30x^2+80x-210=0

a = 30; b = 80; c = -210;
Δ = b2-4ac
Δ = 802-4·30·(-210)
Δ = 31600
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:

$\sqrt{\Delta}=\sqrt{31600}=\sqrt{400*79}=\sqrt{400}*\sqrt{79}=20\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-20\sqrt{79}}{2*30}=\frac{-80-20\sqrt{79}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+20\sqrt{79}}{2*30}=\frac{-80+20\sqrt{79}}{60}
$