2/3x+3/7x=26

Solution for 2/3x+3/7x=26 equation:

2/3x+3/7x=26

We move all terms to the left:

2/3x+3/7x-(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+9x/21x^2-26=0

We multiply all the terms by the denominator


14x+9x-26*21x^2=0

We add all the numbers together, and all the variables

23x-26*21x^2=0

Wy multiply elements

-546x^2+23x=0

a = -546; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-546)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-546}=\frac{-46}{-1092}
=23/546
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-546}=\frac{0}{-1092}
=0
$