x^2-x-8=-3x^2

Solution for x^2-x-8=-3x^2 equation:

x^2-x-8=-3x^2

We move all terms to the left:

x^2-x-8-(-3x^2)=0

We add all the numbers together, and all the variables

x^2-(-3x^2)-1x-8=0

We get rid of parentheses

x^2+3x^2-1x-8=0

We add all the numbers together, and all the variables

4x^2-1x-8=0

a = 4; b = -1; c = -8;
Δ = b2-4ac
Δ = -12-4·4·(-8)
Δ = 129
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{-(-1)-\sqrt{129}}{2*4}=\frac{1-\sqrt{129}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{129}}{2*4}=\frac{1+\sqrt{129}}{8}
$