14-1/5z=1/2z

Solution for 14-1/5z=1/2z equation:

14-1/5z=1/2z

We move all terms to the left:

14-1/5z-(1/2z)=0


Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R



Domain of the equation: 2z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

-1/5z-(+1/2z)+14=0

We get rid of parentheses

-1/5z-1/2z+14=0

We calculate fractions


(-2z)/10z^2+(-5z)/10z^2+14=0

We multiply all the terms by the denominator


(-2z)+(-5z)+14*10z^2=0

Wy multiply elements

140z^2+(-2z)+(-5z)=0

We get rid of parentheses

140z^2-2z-5z=0

We add all the numbers together, and all the variables

140z^2-7z=0

a = 140; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·140·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*140}=\frac{0}{280}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*140}=\frac{14}{280}
=1/20
$