6/7z-2=2/49z

Solution for 6/7z-2=2/49z equation:

6/7z-2=2/49z

We move all terms to the left:

6/7z-2-(2/49z)=0


Domain of the equation: 7z!=0

z!=0/7

z!=0

z∈R



Domain of the equation: 49z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

6/7z-(+2/49z)-2=0

We get rid of parentheses

6/7z-2/49z-2=0

We calculate fractions


294z/343z^2+(-14z)/343z^2-2=0

We multiply all the terms by the denominator


294z+(-14z)-2*343z^2=0

Wy multiply elements

-686z^2+294z+(-14z)=0

We get rid of parentheses

-686z^2+294z-14z=0

We add all the numbers together, and all the variables

-686z^2+280z=0

a = -686; b = 280; c = 0;
Δ = b2-4ac
Δ = 2802-4·(-686)·0
Δ = 78400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{78400}=280$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-280}{2*-686}=\frac{-560}{-1372}
=20/49
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+280}{2*-686}=\frac{0}{-1372}
=0
$