17x^2-51x-36=0

Solution for 17x^2-51x-36=0 equation:

17x^2-51x-36=0

a = 17; b = -51; c = -36;
Δ = b2-4ac
Δ = -512-4·17·(-36)
Δ = 5049
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:

$\sqrt{\Delta}=\sqrt{5049}=\sqrt{9*561}=\sqrt{9}*\sqrt{561}=3\sqrt{561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-3\sqrt{561}}{2*17}=\frac{51-3\sqrt{561}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3\sqrt{561}}{2*17}=\frac{51+3\sqrt{561}}{34}
$