3x^2-9x=11

Solution for 3x^2-9x=11 equation:

3x^2-9x=11

We move all terms to the left:

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

a = 3; b = -9; c = -11;
Δ = b2-4ac
Δ = -92-4·3·(-11)
Δ = 213
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{-(-9)-\sqrt{213}}{2*3}=\frac{9-\sqrt{213}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{213}}{2*3}=\frac{9+\sqrt{213}}{6}
$