(5x+15)(6x-10)=180

Solution for (5x+15)(6x-10)=180 equation:

(5x+15)(6x-10)=180

We move all terms to the left:

(5x+15)(6x-10)-(180)=0

We multiply parentheses ..

(+30x^2-50x+90x-150)-180=0

We get rid of parentheses

30x^2-50x+90x-150-180=0

We add all the numbers together, and all the variables

30x^2+40x-330=0

a = 30; b = 40; c = -330;
Δ = b2-4ac
Δ = 402-4·30·(-330)
Δ = 41200
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:

$\sqrt{\Delta}=\sqrt{41200}=\sqrt{400*103}=\sqrt{400}*\sqrt{103}=20\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-20\sqrt{103}}{2*30}=\frac{-40-20\sqrt{103}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+20\sqrt{103}}{2*30}=\frac{-40+20\sqrt{103}}{60}
$