9x^2=24x-6

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

9x^2=24x-6

We move all terms to the left:

9x^2-(24x-6)=0

We get rid of parentheses

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}
$