4z(6z-4)=76

Solution for 4z(6z-4)=76 equation:

4z(6z-4)=76

We move all terms to the left:

4z(6z-4)-(76)=0

We multiply parentheses

24z^2-16z-76=0

a = 24; b = -16; c = -76;
Δ = b2-4ac
Δ = -162-4·24·(-76)
Δ = 7552
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:

$\sqrt{\Delta}=\sqrt{7552}=\sqrt{64*118}=\sqrt{64}*\sqrt{118}=8\sqrt{118}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{118}}{2*24}=\frac{16-8\sqrt{118}}{48}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{118}}{2*24}=\frac{16+8\sqrt{118}}{48}
$