-4/7-8/35x+1/5x=-42

Solution for -4/7-8/35x+1/5x=-42 equation:

-4/7-8/35x+1/5x=-42

We move all terms to the left:

-4/7-8/35x+1/5x-(-42)=0


Domain of the equation: 35x!=0

x!=0/35

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-8/35x+1/5x+42-4/7=0

We calculate fractions


(-3500x^2)/8575x^2+(-1960x)/8575x^2+1715x/8575x^2+42=0

We multiply all the terms by the denominator


(-3500x^2)+(-1960x)+1715x+42*8575x^2=0

We add all the numbers together, and all the variables

(-3500x^2)+1715x+(-1960x)+42*8575x^2=0

Wy multiply elements

(-3500x^2)+360150x^2+1715x+(-1960x)=0

We get rid of parentheses

-3500x^2+360150x^2+1715x-1960x=0

We add all the numbers together, and all the variables

356650x^2-245x=0

a = 356650; b = -245; c = 0;
Δ = b2-4ac
Δ = -2452-4·356650·0
Δ = 60025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{60025}=245$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-245)-245}{2*356650}=\frac{0}{713300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-245)+245}{2*356650}=\frac{490}{713300}
=7/10190
$