7z^2+12z-27=0

Solution for 7z^2+12z-27=0 equation:

7z^2+12z-27=0

a = 7; b = 12; c = -27;
Δ = b2-4ac
Δ = 122-4·7·(-27)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-30}{2*7}=\frac{-42}{14}
=-3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+30}{2*7}=\frac{18}{14}
=1+2/7
$