-8+z(7/2+-4)=5z+-4

Solution for -8+z(7/2+-4)=5z+-4 equation:

-8+z(7/2+-4)=5z+-4

We move all terms to the left:

-8+z(7/2+-4)-(5z+-4)=0

We add all the numbers together, and all the variables

z(7/2-4)-(5z-4)-8=0

We multiply parentheses

7z^2-4z-(5z-4)-8=0

We get rid of parentheses

7z^2-4z-5z+4-8=0

We add all the numbers together, and all the variables

7z^2-9z-4=0

a = 7; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·7·(-4)
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{193}}{2*7}=\frac{9-\sqrt{193}}{14}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{193}}{2*7}=\frac{9+\sqrt{193}}{14}
$