x^2+5x+6=120

Solution for x^2+5x+6=120 equation:

x^2+5x+6=120

We move all terms to the left:

x^2+5x+6-(120)=0

We add all the numbers together, and all the variables

x^2+5x-114=0

a = 1; b = 5; c = -114;
Δ = b2-4ac
Δ = 52-4·1·(-114)
Δ = 481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{481}}{2*1}=\frac{-5-\sqrt{481}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{481}}{2*1}=\frac{-5+\sqrt{481}}{2}
$