10-6x-9x^2=-9

Solution for 10-6x-9x^2=-9 equation:

10-6x-9x^2=-9

We move all terms to the left:

10-6x-9x^2-(-9)=0

We add all the numbers together, and all the variables

-9x^2-6x+19=0

a = -9; b = -6; c = +19;
Δ = b2-4ac
Δ = -62-4·(-9)·19
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12\sqrt{5}}{2*-9}=\frac{6-12\sqrt{5}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12\sqrt{5}}{2*-9}=\frac{6+12\sqrt{5}}{-18}
$