4z^2/2z+3=30

Solution for 4z^2/2z+3=30 equation:

4z^2/2z+3=30

We move all terms to the left:

4z^2/2z+3-(30)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We add all the numbers together, and all the variables

4z^2/2z-27=0

We multiply all the terms by the denominator


4z^2-27*2z=0

Wy multiply elements

4z^2-54z=0

a = 4; b = -54; c = 0;
Δ = b2-4ac
Δ = -542-4·4·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54}{2*4}=\frac{0}{8}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54}{2*4}=\frac{108}{8}
=13+1/2
$