2x^2+12x+20=164

Solution for 2x^2+12x+20=164 equation:

2x^2+12x+20=164

We move all terms to the left:

2x^2+12x+20-(164)=0

We add all the numbers together, and all the variables

2x^2+12x-144=0

a = 2; b = 12; c = -144;
Δ = b2-4ac
Δ = 122-4·2·(-144)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-36}{2*2}=\frac{-48}{4}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+36}{2*2}=\frac{24}{4}
=6
$