38a^2+31a-112=-7a+8a^2

Solution for 38a^2+31a-112=-7a+8a^2 equation:

38a^2+31a-112=-7a+8a^2

We move all terms to the left:

38a^2+31a-112-(-7a+8a^2)=0

We get rid of parentheses

38a^2-8a^2+7a+31a-112=0

We add all the numbers together, and all the variables

30a^2+38a-112=0

a = 30; b = 38; c = -112;
Δ = b2-4ac
Δ = 382-4·30·(-112)
Δ = 14884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14884}=122$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-122}{2*30}=\frac{-160}{60}
=-2+2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+122}{2*30}=\frac{84}{60}
=1+2/5
$