-5/7x-2/35x+1/5=-40

Solution for -5/7x-2/35x+1/5=-40 equation:

-5/7x-2/35x+1/5=-40

We move all terms to the left:

-5/7x-2/35x+1/5-(-40)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 35x!=0

x!=0/35

x!=0

x∈R


We add all the numbers together, and all the variables

-5/7x-2/35x+40+1/5=0

We calculate fractions


735x^2/6125x^2+(-4375x)/6125x^2+(-350x)/6125x^2+40=0

We multiply all the terms by the denominator


735x^2+(-4375x)+(-350x)+40*6125x^2=0

Wy multiply elements

735x^2+245000x^2+(-4375x)+(-350x)=0

We get rid of parentheses

735x^2+245000x^2-4375x-350x=0

We add all the numbers together, and all the variables

245735x^2-4725x=0

a = 245735; b = -4725; c = 0;
Δ = b2-4ac
Δ = -47252-4·245735·0
Δ = 22325625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22325625}=4725$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4725)-4725}{2*245735}=\frac{0}{491470}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4725)+4725}{2*245735}=\frac{9450}{491470}
=135/7021
$