14z-4z^2=8

Solution for 14z-4z^2=8 equation:

14z-4z^2=8

We move all terms to the left:

14z-4z^2-(8)=0

a = -4; b = 14; c = -8;
Δ = b2-4ac
Δ = 142-4·(-4)·(-8)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{17}}{2*-4}=\frac{-14-2\sqrt{17}}{-8}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{17}}{2*-4}=\frac{-14+2\sqrt{17}}{-8}
$