z^2-3z=22.75

Solution for z^2-3z=22.75 equation:

z^2-3z=22.75

We move all terms to the left:

z^2-3z-(22.75)=0

We add all the numbers together, and all the variables

z^2-3z-22.75=0

a = 1; b = -3; c = -22.75;
Δ = b2-4ac
Δ = -32-4·1·(-22.75)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-10}{2*1}=\frac{-7}{2}
=-3+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+10}{2*1}=\frac{13}{2}
=6+1/2
$