18x^2+9x-38=0

Solution for 18x^2+9x-38=0 equation:

18x^2+9x-38=0

a = 18; b = 9; c = -38;
Δ = b2-4ac
Δ = 92-4·18·(-38)
Δ = 2817
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:

$\sqrt{\Delta}=\sqrt{2817}=\sqrt{9*313}=\sqrt{9}*\sqrt{313}=3\sqrt{313}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{313}}{2*18}=\frac{-9-3\sqrt{313}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{313}}{2*18}=\frac{-9+3\sqrt{313}}{36}
$