(2x+30)(2x+18)=120

Solution for (2x+30)(2x+18)=120 equation:

(2x+30)(2x+18)=120

We move all terms to the left:

(2x+30)(2x+18)-(120)=0

We multiply parentheses ..

(+4x^2+36x+60x+540)-120=0

We get rid of parentheses

4x^2+36x+60x+540-120=0

We add all the numbers together, and all the variables

4x^2+96x+420=0

a = 4; b = 96; c = +420;
Δ = b2-4ac
Δ = 962-4·4·420
Δ = 2496
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:

$\sqrt{\Delta}=\sqrt{2496}=\sqrt{64*39}=\sqrt{64}*\sqrt{39}=8\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-8\sqrt{39}}{2*4}=\frac{-96-8\sqrt{39}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+8\sqrt{39}}{2*4}=\frac{-96+8\sqrt{39}}{8}
$