5x=x^2-3

Solution for 5x=x^2-3 equation:

5x=x^2-3

We move all terms to the left:

5x-(x^2-3)=0

We get rid of parentheses

-x^2+5x+3=0

We add all the numbers together, and all the variables

-1x^2+5x+3=0

a = -1; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·(-1)·3
Δ = 37
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{37}}{2*-1}=\frac{-5-\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*-1}=\frac{-5+\sqrt{37}}{-2}
$