15x(x+5)=150

Solution for 15x(x+5)=150 equation:

15x(x+5)=150

We move all terms to the left:

15x(x+5)-(150)=0

We multiply parentheses

15x^2+75x-150=0

a = 15; b = 75; c = -150;
Δ = b2-4ac
Δ = 752-4·15·(-150)
Δ = 14625
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:

$\sqrt{\Delta}=\sqrt{14625}=\sqrt{225*65}=\sqrt{225}*\sqrt{65}=15\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-15\sqrt{65}}{2*15}=\frac{-75-15\sqrt{65}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+15\sqrt{65}}{2*15}=\frac{-75+15\sqrt{65}}{30}
$