18x^2-69x-15=0

Solution for 18x^2-69x-15=0 equation:

18x^2-69x-15=0

a = 18; b = -69; c = -15;
Δ = b2-4ac
Δ = -692-4·18·(-15)
Δ = 5841
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:

$\sqrt{\Delta}=\sqrt{5841}=\sqrt{9*649}=\sqrt{9}*\sqrt{649}=3\sqrt{649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-3\sqrt{649}}{2*18}=\frac{69-3\sqrt{649}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+3\sqrt{649}}{2*18}=\frac{69+3\sqrt{649}}{36}
$