X2-9=3x-1

Solution for X2-9=3x-1 equation:

X2-9=3X-1

We move all terms to the left:

X2-9-(3X-1)=0

We add all the numbers together, and all the variables

X^2-(3X-1)-9=0

We get rid of parentheses

X^2-3X+1-9=0

We add all the numbers together, and all the variables

X^2-3X-8=0

a = 1; b = -3; c = -8;
Δ = b2-4ac
Δ = -32-4·1·(-8)
Δ = 41
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{-(-3)-\sqrt{41}}{2*1}=\frac{3-\sqrt{41}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{41}}{2*1}=\frac{3+\sqrt{41}}{2}
$