4x-3=x2-1

Solution for 4x-3=x2-1 equation:

4x-3=x2-1

We move all terms to the left:

4x-3-(x2-1)=0

We add all the numbers together, and all the variables

-(+x^2-1)+4x-3=0

We get rid of parentheses

-x^2+4x+1-3=0

We add all the numbers together, and all the variables

-1x^2+4x-2=0

a = -1; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·(-1)·(-2)
Δ = 8
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:

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