5x=x^2-2

Solution for 5x=x^2-2 equation:

5x=x^2-2

We move all terms to the left:

5x-(x^2-2)=0

We get rid of parentheses

-x^2+5x+2=0

We add all the numbers together, and all the variables

-1x^2+5x+2=0

a = -1; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·(-1)·2
Δ = 33
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{-(5)-\sqrt{33}}{2*-1}=\frac{-5-\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{33}}{2*-1}=\frac{-5+\sqrt{33}}{-2}
$