3x^2=30x-9

Solution for 3x^2=30x-9 equation:

3x^2=30x-9

We move all terms to the left:

3x^2-(30x-9)=0

We get rid of parentheses

3x^2-30x+9=0

a = 3; b = -30; c = +9;
Δ = b2-4ac
Δ = -302-4·3·9
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{22}}{2*3}=\frac{30-6\sqrt{22}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{22}}{2*3}=\frac{30+6\sqrt{22}}{6}
$