15x(2x+10)=120

Solution for 15x(2x+10)=120 equation:

15x(2x+10)=120

We move all terms to the left:

15x(2x+10)-(120)=0

We multiply parentheses

30x^2+150x-120=0

a = 30; b = 150; c = -120;
Δ = b2-4ac
Δ = 1502-4·30·(-120)
Δ = 36900
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:

$\sqrt{\Delta}=\sqrt{36900}=\sqrt{900*41}=\sqrt{900}*\sqrt{41}=30\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-30\sqrt{41}}{2*30}=\frac{-150-30\sqrt{41}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+30\sqrt{41}}{2*30}=\frac{-150+30\sqrt{41}}{60}
$