a^2=a+112

Solution for a^2=a+112 equation:

a^2=a+112

We move all terms to the left:

a^2-(a+112)=0

We get rid of parentheses

a^2-a-112=0

We add all the numbers together, and all the variables

a^2-1a-112=0

a = 1; b = -1; c = -112;
Δ = b2-4ac
Δ = -12-4·1·(-112)
Δ = 449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{449}}{2*1}=\frac{1-\sqrt{449}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{449}}{2*1}=\frac{1+\sqrt{449}}{2}
$