X2-3=3x+1

Solution for X2-3=3x+1 equation:

X2-3=3X+1

We move all terms to the left:

X2-3-(3X+1)=0

We add all the numbers together, and all the variables

X^2-(3X+1)-3=0

We get rid of parentheses

X^2-3X-1-3=0

We add all the numbers together, and all the variables

X^2-3X-4=0

a = 1; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·1·(-4)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*1}=\frac{8}{2}
=4
$