x^2-3=-3^2+8x

Solution for x^2-3=-3^2+8x equation:

x^2-3=-3^2+8x

We move all terms to the left:

x^2-3-(-3^2+8x)=0

We get rid of parentheses

x^2-8x-3+3^2=0

We add all the numbers together, and all the variables

x^2-8x+6=0

a = 1; b = -8; c = +6;
Δ = b2-4ac
Δ = -82-4·1·6
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{10}}{2*1}=\frac{8-2\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{10}}{2*1}=\frac{8+2\sqrt{10}}{2}
$