x^2=-6x+54

Solution for x^2=-6x+54 equation:

x^2=-6x+54

We move all terms to the left:

x^2-(-6x+54)=0

We get rid of parentheses

x^2+6x-54=0

a = 1; b = 6; c = -54;
Δ = b2-4ac
Δ = 62-4·1·(-54)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{7}}{2*1}=\frac{-6-6\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{7}}{2*1}=\frac{-6+6\sqrt{7}}{2}
$