2/3X-4/7x=26

Solution for 2/3X-4/7x=26 equation:

2/3X-4/7X=26

We move all terms to the left:

2/3X-4/7X-(26)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R



Domain of the equation: 7X!=0

X!=0/7

X!=0

X∈R


We calculate fractions


14X/21X^2+(-12X)/21X^2-26=0

We multiply all the terms by the denominator


14X+(-12X)-26*21X^2=0

Wy multiply elements

-546X^2+14X+(-12X)=0

We get rid of parentheses

-546X^2+14X-12X=0

We add all the numbers together, and all the variables

-546X^2+2X=0

a = -546; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-546)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-546}=\frac{-4}{-1092}
=1/273
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-546}=\frac{0}{-1092}
=0
$