4z^2-z=5

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

4z^2-z=5

We move all terms to the left:

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

We add all the numbers together, and all the variables

4z^2-1z-5=0

a = 4; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·4·(-5)
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*4}=\frac{-8}{8}
=-1
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*4}=\frac{10}{8}
=1+1/4
$