-9x^2+24x-6=0

Solution for -9x^2+24x-6=0 equation:

-9x^2+24x-6=0

a = -9; b = 24; c = -6;
Δ = b2-4ac
Δ = 242-4·(-9)·(-6)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{10}}{2*-9}=\frac{-24-6\sqrt{10}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{10}}{2*-9}=\frac{-24+6\sqrt{10}}{-18}
$