3a^2-39a+9=0

Solution for 3a^2-39a+9=0 equation:

3a^2-39a+9=0

a = 3; b = -39; c = +9;
Δ = b2-4ac
Δ = -392-4·3·9
Δ = 1413
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1413}=\sqrt{9*157}=\sqrt{9}*\sqrt{157}=3\sqrt{157}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-3\sqrt{157}}{2*3}=\frac{39-3\sqrt{157}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+3\sqrt{157}}{2*3}=\frac{39+3\sqrt{157}}{6}
$