18x^2-9x-13=0

Solution for 18x^2-9x-13=0 equation:

18x^2-9x-13=0

a = 18; b = -9; c = -13;
Δ = b2-4ac
Δ = -92-4·18·(-13)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{113}}{2*18}=\frac{9-3\sqrt{113}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{113}}{2*18}=\frac{9+3\sqrt{113}}{36}
$