x+2x2=8x-2

Solution for x+2x2=8x-2 equation:

x+2x^2=8x-2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-7x+2=0

a = 2; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·2·2
Δ = 33
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{-(-7)-\sqrt{33}}{2*2}=\frac{7-\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{33}}{2*2}=\frac{7+\sqrt{33}}{4}
$