X^2-7=x-2x^2

Solution for X^2-7=x-2x^2 equation:

X^2-7=X-2X^2

We move all terms to the left:

X^2-7-(X-2X^2)=0

We get rid of parentheses

X^2+2X^2-X-7=0

We add all the numbers together, and all the variables

3X^2-1X-7=0

a = 3; b = -1; c = -7;
Δ = b2-4ac
Δ = -12-4·3·(-7)
Δ = 85
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{85}}{2*3}=\frac{1-\sqrt{85}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{85}}{2*3}=\frac{1+\sqrt{85}}{6}
$