1/5x+2=4-2/7x

Solution for 1/5x+2=4-2/7x equation:

1/5x+2=4-2/7x

We move all terms to the left:

1/5x+2-(4-2/7x)=0


Domain of the equation: 5x!=0

x!=0/5

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

1/5x-(-2/7x+4)+2=0

We get rid of parentheses

1/5x+2/7x-4+2=0

We calculate fractions


7x/35x^2+10x/35x^2-4+2=0

We add all the numbers together, and all the variables

7x/35x^2+10x/35x^2-2=0

We multiply all the terms by the denominator


7x+10x-2*35x^2=0

We add all the numbers together, and all the variables

17x-2*35x^2=0

Wy multiply elements

-70x^2+17x=0

a = -70; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-70)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-70}=\frac{-34}{-140}
=17/70
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-70}=\frac{0}{-140}
=0
$