10z^2+33z-7=0

Solution for 10z^2+33z-7=0 equation:

10z^2+33z-7=0

a = 10; b = 33; c = -7;
Δ = b2-4ac
Δ = 332-4·10·(-7)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-37}{2*10}=\frac{-70}{20}
=-3+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+37}{2*10}=\frac{4}{20}
=1/5
$