x=-x^2+28

Solution for x=-x^2+28 equation:

x=-x^2+28

We move all terms to the left:

x-(-x^2+28)=0

We get rid of parentheses

x^2+x-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}
$