5z^2-z=4

Solution for 5z^2-z=4 equation:

5z^2-z=4

We move all terms to the left:

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

We add all the numbers together, and all the variables

5z^2-1z-4=0

a = 5; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·5·(-4)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*5}=\frac{-8}{10}
=-4/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*5}=\frac{10}{10}
=1
$