(5x+15)(6x-2)=90

Solution for (5x+15)(6x-2)=90 equation:

(5x+15)(6x-2)=90

We move all terms to the left:

(5x+15)(6x-2)-(90)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

30x^2+80x-120=0

a = 30; b = 80; c = -120;
Δ = b2-4ac
Δ = 802-4·30·(-120)
Δ = 20800
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:

$\sqrt{\Delta}=\sqrt{20800}=\sqrt{1600*13}=\sqrt{1600}*\sqrt{13}=40\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-40\sqrt{13}}{2*30}=\frac{-80-40\sqrt{13}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+40\sqrt{13}}{2*30}=\frac{-80+40\sqrt{13}}{60}
$