18x^2+3x-13=0

Solution for 18x^2+3x-13=0 equation:

18x^2+3x-13=0

a = 18; b = 3; c = -13;
Δ = b2-4ac
Δ = 32-4·18·(-13)
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{105}}{2*18}=\frac{-3-3\sqrt{105}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{105}}{2*18}=\frac{-3+3\sqrt{105}}{36}
$