-1/3x+5=-2+5/7x

Solution for -1/3x+5=-2+5/7x equation:

-1/3x+5=-2+5/7x

We move all terms to the left:

-1/3x+5-(-2+5/7x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/3x-(5/7x-2)+5=0

We get rid of parentheses

-1/3x-5/7x+2+5=0

We calculate fractions


(-7x)/21x^2+(-15x)/21x^2+2+5=0

We add all the numbers together, and all the variables

(-7x)/21x^2+(-15x)/21x^2+7=0

We multiply all the terms by the denominator


(-7x)+(-15x)+7*21x^2=0

Wy multiply elements

147x^2+(-7x)+(-15x)=0

We get rid of parentheses

147x^2-7x-15x=0

We add all the numbers together, and all the variables

147x^2-22x=0

a = 147; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·147·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*147}=\frac{0}{294}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*147}=\frac{44}{294}
=22/147
$