7z^2-33z-340=0

Solution for 7z^2-33z-340=0 equation:

7z^2-33z-340=0

a = 7; b = -33; c = -340;
Δ = b2-4ac
Δ = -332-4·7·(-340)
Δ = 10609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10609}=103$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-103}{2*7}=\frac{-70}{14}
=-5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+103}{2*7}=\frac{136}{14}
=9+5/7
$