3x^2-32x+81=0

Solution for 3x^2-32x+81=0 equation:

3x^2-32x+81=0

a = 3; b = -32; c = +81;
Δ = b2-4ac
Δ = -322-4·3·81
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{13}}{2*3}=\frac{32-2\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{13}}{2*3}=\frac{32+2\sqrt{13}}{6}
$