18x2-14x-17=0

Solution for 18x2-14x-17=0 equation:

18x^2-14x-17=0

a = 18; b = -14; c = -17;
Δ = b2-4ac
Δ = -142-4·18·(-17)
Δ = 1420
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:

$\sqrt{\Delta}=\sqrt{1420}=\sqrt{4*355}=\sqrt{4}*\sqrt{355}=2\sqrt{355}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{355}}{2*18}=\frac{14-2\sqrt{355}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{355}}{2*18}=\frac{14+2\sqrt{355}}{36}
$