2z(z-4)=43

Solution for 2z(z-4)=43 equation:

2z(z-4)=43

We move all terms to the left:

2z(z-4)-(43)=0

We multiply parentheses

2z^2-8z-43=0

a = 2; b = -8; c = -43;
Δ = b2-4ac
Δ = -82-4·2·(-43)
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{102}}{2*2}=\frac{8-2\sqrt{102}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{102}}{2*2}=\frac{8+2\sqrt{102}}{4}
$