2x^2+2x+13=8x2-4x+1

Solution for 2x^2+2x+13=8x2-4x+1 equation:

2x^2+2x+13=8x^2-4x+1

We move all terms to the left:

2x^2+2x+13-(8x^2-4x+1)=0

We get rid of parentheses

2x^2-8x^2+2x+4x-1+13=0

We add all the numbers together, and all the variables

-6x^2+6x+12=0

a = -6; b = 6; c = +12;
Δ = b2-4ac
Δ = 62-4·(-6)·12
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*-6}=\frac{-24}{-12}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*-6}=\frac{12}{-12}
=-1
$