17(4-z)6z=-20

Solution for 17(4-z)6z=-20 equation:

17(4-z)6z=-20

We move all terms to the left:

17(4-z)6z-(-20)=0

We add all the numbers together, and all the variables

17(-1z+4)6z-(-20)=0

We add all the numbers together, and all the variables

17(-1z+4)6z+20=0

We multiply parentheses

-102z^2+408z+20=0

a = -102; b = 408; c = +20;
Δ = b2-4ac
Δ = 4082-4·(-102)·20
Δ = 174624
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:

$\sqrt{\Delta}=\sqrt{174624}=\sqrt{16*10914}=\sqrt{16}*\sqrt{10914}=4\sqrt{10914}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(408)-4\sqrt{10914}}{2*-102}=\frac{-408-4\sqrt{10914}}{-204}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(408)+4\sqrt{10914}}{2*-102}=\frac{-408+4\sqrt{10914}}{-204}
$