35z^2-102z-32=0

Solution for 35z^2-102z-32=0 equation:

35z^2-102z-32=0

a = 35; b = -102; c = -32;
Δ = b2-4ac
Δ = -1022-4·35·(-32)
Δ = 14884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14884}=122$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-122}{2*35}=\frac{-20}{70}
=-2/7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+122}{2*35}=\frac{224}{70}
=3+1/5
$