8z(14z-7)=180

Solution for 8z(14z-7)=180 equation:

8z(14z-7)=180

We move all terms to the left:

8z(14z-7)-(180)=0

We multiply parentheses

112z^2-56z-180=0

a = 112; b = -56; c = -180;
Δ = b2-4ac
Δ = -562-4·112·(-180)
Δ = 83776
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:

$\sqrt{\Delta}=\sqrt{83776}=\sqrt{64*1309}=\sqrt{64}*\sqrt{1309}=8\sqrt{1309}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{1309}}{2*112}=\frac{56-8\sqrt{1309}}{224}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{1309}}{2*112}=\frac{56+8\sqrt{1309}}{224}
$