12x^2-11=-9x

Solution for 12x^2-11=-9x equation:

12x^2-11=-9x

We move all terms to the left:

12x^2-11-(-9x)=0

We get rid of parentheses

12x^2+9x-11=0

a = 12; b = 9; c = -11;
Δ = b2-4ac
Δ = 92-4·12·(-11)
Δ = 609
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{609}}{2*12}=\frac{-9-\sqrt{609}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{609}}{2*12}=\frac{-9+\sqrt{609}}{24}
$