X=2-2x2+8x

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

X=2-2X^2+8X

We move all terms to the left:

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

We get rid of parentheses

2X^2-8X+X-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 = 65
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{65}}{2*2}=\frac{7-\sqrt{65}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{65}}{2*2}=\frac{7+\sqrt{65}}{4}
$