5x(x+15)+30=120

Solution for 5x(x+15)+30=120 equation:

5x(x+15)+30=120

We move all terms to the left:

5x(x+15)+30-(120)=0

We add all the numbers together, and all the variables

5x(x+15)-90=0

We multiply parentheses

5x^2+75x-90=0

a = 5; b = 75; c = -90;
Δ = b2-4ac
Δ = 752-4·5·(-90)
Δ = 7425
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:

$\sqrt{\Delta}=\sqrt{7425}=\sqrt{225*33}=\sqrt{225}*\sqrt{33}=15\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-15\sqrt{33}}{2*5}=\frac{-75-15\sqrt{33}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+15\sqrt{33}}{2*5}=\frac{-75+15\sqrt{33}}{10}
$