9-11x2=3x

Solution for 9-11x2=3x equation:

9-11x^2=3x

We move all terms to the left:

9-11x^2-(3x)=0

a = -11; b = -3; c = +9;
Δ = b2-4ac
Δ = -32-4·(-11)·9
Δ = 405
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9\sqrt{5}}{2*-11}=\frac{3-9\sqrt{5}}{-22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9\sqrt{5}}{2*-11}=\frac{3+9\sqrt{5}}{-22}
$