27X^2-72x+13=0

Solution for 27X^2-72x+13=0 equation:

27X^2-72X+13=0

a = 27; b = -72; c = +13;
Δ = b2-4ac
Δ = -722-4·27·13
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-6\sqrt{105}}{2*27}=\frac{72-6\sqrt{105}}{54}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+6\sqrt{105}}{2*27}=\frac{72+6\sqrt{105}}{54}
$