2a^2+2a=112

Solution for 2a^2+2a=112 equation:

2a^2+2a=112

We move all terms to the left:

2a^2+2a-(112)=0

a = 2; b = 2; c = -112;
Δ = b2-4ac
Δ = 22-4·2·(-112)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-30}{2*2}=\frac{-32}{4}
=-8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+30}{2*2}=\frac{28}{4}
=7
$