11x=3x2-9

Solution for 11x=3x2-9 equation:

11x=3x^2-9

We move all terms to the left:

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

We get rid of parentheses

-3x^2+11x+9=0

a = -3; b = 11; c = +9;
Δ = b2-4ac
Δ = 112-4·(-3)·9
Δ = 229
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{-(11)-\sqrt{229}}{2*-3}=\frac{-11-\sqrt{229}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{229}}{2*-3}=\frac{-11+\sqrt{229}}{-6}
$