5z+1/2z=1/2z+10

Solution for 5z+1/2z=1/2z+10 equation:

5z+1/2z=1/2z+10

We move all terms to the left:

5z+1/2z-(1/2z+10)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: 2z+10)!=0

z∈R


We get rid of parentheses

5z+1/2z-1/2z-10=0

We multiply all the terms by the denominator


5z*2z-10*2z+1-1=0

We add all the numbers together, and all the variables

5z*2z-10*2z=0

Wy multiply elements

10z^2-20z=0

a = 10; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·10·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*10}=\frac{0}{20}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*10}=\frac{40}{20}
=2
$