x=11-2x^2

Solution for x=11-2x^2 equation:

x=11-2x^2

We move all terms to the left:

x-(11-2x^2)=0

We get rid of parentheses

2x^2+x-11=0

a = 2; b = 1; c = -11;
Δ = b2-4ac
Δ = 12-4·2·(-11)
Δ = 89
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{89}}{2*2}=\frac{-1-\sqrt{89}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{89}}{2*2}=\frac{-1+\sqrt{89}}{4}
$