z^2/z=35

Solution for z^2/z=35 equation:

z^2/z=35

We move all terms to the left:

z^2/z-(35)=0


Domain of the equation: z!=0

z∈R


We multiply all the terms by the denominator


z^2-35*z=0

We add all the numbers together, and all the variables

z^2-35z=0

a = 1; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·1·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*1}=\frac{0}{2}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*1}=\frac{70}{2}
=35
$