5x^2-18x+13.5=0

Solution for 5x^2-18x+13.5=0 equation:

5x^2-18x+13.5=0

a = 5; b = -18; c = +13.5;
Δ = b2-4ac
Δ = -182-4·5·13.5
Δ = 54
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:

$\sqrt{\Delta}=\sqrt{54}=\sqrt{9*6}=\sqrt{9}*\sqrt{6}=3\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-3\sqrt{6}}{2*5}=\frac{18-3\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+3\sqrt{6}}{2*5}=\frac{18+3\sqrt{6}}{10}
$