15x^2-10x-20=0

Solution for 15x^2-10x-20=0 equation:

15x^2-10x-20=0

a = 15; b = -10; c = -20;
Δ = b2-4ac
Δ = -102-4·15·(-20)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{13}}{2*15}=\frac{10-10\sqrt{13}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{13}}{2*15}=\frac{10+10\sqrt{13}}{30}
$