X2-5=2x+3

Solution for X2-5=2x+3 equation:

X2-5=2X+3

We move all terms to the left:

X2-5-(2X+3)=0

We add all the numbers together, and all the variables

X^2-(2X+3)-5=0

We get rid of parentheses

X^2-2X-3-5=0

We add all the numbers together, and all the variables

X^2-2X-8=0

a = 1; b = -2; c = -8;
Δ = b2-4ac
Δ = -22-4·1·(-8)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*1}=\frac{-4}{2}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*1}=\frac{8}{2}
=4
$