15z^2-31z+12=0

Solution for 15z^2-31z+12=0 equation:

15z^2-31z+12=0

a = 15; b = -31; c = +12;
Δ = b2-4ac
Δ = -312-4·15·12
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{241}}{2*15}=\frac{31-\sqrt{241}}{30}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{241}}{2*15}=\frac{31+\sqrt{241}}{30}
$