2a^2+4a=126

Solution for 2a^2+4a=126 equation:

2a^2+4a=126

We move all terms to the left:

2a^2+4a-(126)=0

a = 2; b = 4; c = -126;
Δ = b2-4ac
Δ = 42-4·2·(-126)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-32}{2*2}=\frac{-36}{4}
=-9
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+32}{2*2}=\frac{28}{4}
=7
$