x^2-(413+4x)=112

Solution for x^2-(413+4x)=112 equation:

x^2-(413+4x)=112

We move all terms to the left:

x^2-(413+4x)-(112)=0

We add all the numbers together, and all the variables

x^2-(4x+413)-112=0

We get rid of parentheses

x^2-4x-413-112=0

We add all the numbers together, and all the variables

x^2-4x-525=0

a = 1; b = -4; c = -525;
Δ = b2-4ac
Δ = -42-4·1·(-525)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-46}{2*1}=\frac{-42}{2}
=-21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+46}{2*1}=\frac{50}{2}
=25
$