7z^2+12z-20=0

Solution for 7z^2+12z-20=0 equation:

7z^2+12z-20=0

a = 7; b = 12; c = -20;
Δ = b2-4ac
Δ = 122-4·7·(-20)
Δ = 704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{11}}{2*7}=\frac{-12-8\sqrt{11}}{14}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{11}}{2*7}=\frac{-12+8\sqrt{11}}{14}
$