-3x^2-11x=9

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

-3x^2-11x=9

We move all terms to the left:

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

a = -3; b = -11; c = -9;
Δ = b2-4ac
Δ = -112-4·(-3)·(-9)
Δ = 13
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{13}}{2*-3}=\frac{11-\sqrt{13}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{13}}{2*-3}=\frac{11+\sqrt{13}}{-6}
$