4/5z+2=7/10z

Solution for 4/5z+2=7/10z equation:

4/5z+2=7/10z

We move all terms to the left:

4/5z+2-(7/10z)=0


Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R



Domain of the equation: 10z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

4/5z-(+7/10z)+2=0

We get rid of parentheses

4/5z-7/10z+2=0

We calculate fractions


40z/50z^2+(-35z)/50z^2+2=0

We multiply all the terms by the denominator


40z+(-35z)+2*50z^2=0

Wy multiply elements

100z^2+40z+(-35z)=0

We get rid of parentheses

100z^2+40z-35z=0

We add all the numbers together, and all the variables

100z^2+5z=0

a = 100; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·100·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*100}=\frac{-10}{200}
=-1/20
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*100}=\frac{0}{200}
=0
$