27x^2-48x+13=0

Solution for 27x^2-48x+13=0 equation:

27x^2-48x+13=0

a = 27; b = -48; c = +13;
Δ = b2-4ac
Δ = -482-4·27·13
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-30}{2*27}=\frac{18}{54}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+30}{2*27}=\frac{78}{54}
=1+4/9
$