4/7z+2/3z=3

Solution for 4/7z+2/3z=3 equation:

4/7z+2/3z=3

We move all terms to the left:

4/7z+2/3z-(3)=0


Domain of the equation: 7z!=0

z!=0/7

z!=0

z∈R



Domain of the equation: 3z!=0

z!=0/3

z!=0

z∈R


We calculate fractions


12z/21z^2+14z/21z^2-3=0

We multiply all the terms by the denominator


12z+14z-3*21z^2=0

We add all the numbers together, and all the variables

26z-3*21z^2=0

Wy multiply elements

-63z^2+26z=0

a = -63; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·(-63)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*-63}=\frac{-52}{-126}
=26/63
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*-63}=\frac{0}{-126}
=0
$