15x^2-10x-17=0

Solution for 15x^2-10x-17=0 equation:

15x^2-10x-17=0

a = 15; b = -10; c = -17;
Δ = b2-4ac
Δ = -102-4·15·(-17)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{70}}{2*15}=\frac{10-4\sqrt{70}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{70}}{2*15}=\frac{10+4\sqrt{70}}{30}
$