2x-3=x2-3

Solution for 2x-3=x2-3 equation:

2x-3=x2-3

We move all terms to the left:

2x-3-(x2-3)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+2x=0

a = -1; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-1)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-1}=\frac{0}{-2}
=0
$