8z2-68z=-32

Solution for 8z2-68z=-32 equation:

8z^2-68z=-32

We move all terms to the left:

8z^2-68z-(-32)=0

We add all the numbers together, and all the variables

8z^2-68z+32=0

a = 8; b = -68; c = +32;
Δ = b2-4ac
Δ = -682-4·8·32
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-60}{2*8}=\frac{8}{16}
=1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+60}{2*8}=\frac{128}{16}
=8
$