-2/3x+4/5+3/7x=59/105

Solution for -2/3x+4/5+3/7x=59/105 equation:

-2/3x+4/5+3/7x=59/105

We move all terms to the left:

-2/3x+4/5+3/7x-(59/105)=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 add all the numbers together, and all the variables

-2/3x+3/7x+4/5-(+59/105)=0

We get rid of parentheses

-2/3x+3/7x+4/5-59/105=0

We calculate fractions


(-43365x^2)/55125x^2+61740x^2/55125x^2+(-36750x)/55125x^2+23625x/55125x^2=0

We multiply all the terms by the denominator


(-43365x^2)+61740x^2+(-36750x)+23625x=0

We add all the numbers together, and all the variables

61740x^2+(-43365x^2)+23625x+(-36750x)=0

We get rid of parentheses

61740x^2-43365x^2+23625x-36750x=0

We add all the numbers together, and all the variables

18375x^2-13125x=0

a = 18375; b = -13125; c = 0;
Δ = b2-4ac
Δ = -131252-4·18375·0
Δ = 172265625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{172265625}=13125$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13125)-13125}{2*18375}=\frac{0}{36750}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13125)+13125}{2*18375}=\frac{26250}{36750}
=5/7
$