x^2+x=x+24

Solution for x^2+x=x+24 equation:

x^2+x=x+24

We move all terms to the left:

x^2+x-(x+24)=0

We get rid of parentheses

x^2+x-x-24=0

We add all the numbers together, and all the variables

x^2-24=0

a = 1; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·1·(-24)
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*1}=\frac{0-4\sqrt{6}}{2}
=-\frac{4\sqrt{6}}{2}
=-2\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*1}=\frac{0+4\sqrt{6}}{2}
=\frac{4\sqrt{6}}{2}
=2\sqrt{6}
$