15z^2-3z+10z-2=0

Solution for 15z^2-3z+10z-2=0 equation:

15z^2-3z+10z-2=0

We add all the numbers together, and all the variables

15z^2+7z-2=0

a = 15; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·15·(-2)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*15}=\frac{-20}{30}
=-2/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*15}=\frac{6}{30}
=1/5
$