(2x+4)(2x+11)=120

Solution for (2x+4)(2x+11)=120 equation:

(2x+4)(2x+11)=120

We move all terms to the left:

(2x+4)(2x+11)-(120)=0

We multiply parentheses ..

(+4x^2+22x+8x+44)-120=0

We get rid of parentheses

4x^2+22x+8x+44-120=0

We add all the numbers together, and all the variables

4x^2+30x-76=0

a = 4; b = 30; c = -76;
Δ = b2-4ac
Δ = 302-4·4·(-76)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-46}{2*4}=\frac{-76}{8}
=-9+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+46}{2*4}=\frac{16}{8}
=2
$