9x^2=-24x-10

Solution for 9x^2=-24x-10 equation:

9x^2=-24x-10

We move all terms to the left:

9x^2-(-24x-10)=0

We get rid of parentheses

9x^2+24x+10=0

a = 9; b = 24; c = +10;
Δ = b2-4ac
Δ = 242-4·9·10
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{6}}{2*9}=\frac{-24-6\sqrt{6}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{6}}{2*9}=\frac{-24+6\sqrt{6}}{18}
$