-15z^2-34z+15=0

Solution for -15z^2-34z+15=0 equation:

-15z^2-34z+15=0

a = -15; b = -34; c = +15;
Δ = b2-4ac
Δ = -342-4·(-15)·15
Δ = 2056
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:

$\sqrt{\Delta}=\sqrt{2056}=\sqrt{4*514}=\sqrt{4}*\sqrt{514}=2\sqrt{514}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{514}}{2*-15}=\frac{34-2\sqrt{514}}{-30}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{514}}{2*-15}=\frac{34+2\sqrt{514}}{-30}
$