x^2=x+28

Solution for x^2=x+28 equation:

x^2=x+28

We move all terms to the left:

x^2-(x+28)=0

We get rid of parentheses

x^2-x-28=0

We add all the numbers together, and all the variables

x^2-1x-28=0

a = 1; b = -1; c = -28;
Δ = b2-4ac
Δ = -12-4·1·(-28)
Δ = 113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{113}}{2*1}=\frac{1-\sqrt{113}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{113}}{2*1}=\frac{1+\sqrt{113}}{2}
$