15z^2+15z-20=0

Solution for 15z^2+15z-20=0 equation:

15z^2+15z-20=0

a = 15; b = 15; c = -20;
Δ = b2-4ac
Δ = 152-4·15·(-20)
Δ = 1425
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1425}=\sqrt{25*57}=\sqrt{25}*\sqrt{57}=5\sqrt{57}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{57}}{2*15}=\frac{-15-5\sqrt{57}}{30}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{57}}{2*15}=\frac{-15+5\sqrt{57}}{30}
$