2/5x+1=4/7x+10

Solution for 2/5x+1=4/7x+10 equation:

2/5x+1=4/7x+10

We move all terms to the left:

2/5x+1-(4/7x+10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 7x+10)!=0

x∈R


We get rid of parentheses

2/5x-4/7x-10+1=0

We calculate fractions


14x/35x^2+(-20x)/35x^2-10+1=0

We add all the numbers together, and all the variables

14x/35x^2+(-20x)/35x^2-9=0

We multiply all the terms by the denominator


14x+(-20x)-9*35x^2=0

Wy multiply elements

-315x^2+14x+(-20x)=0

We get rid of parentheses

-315x^2+14x-20x=0

We add all the numbers together, and all the variables

-315x^2-6x=0

a = -315; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-315)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-315}=\frac{0}{-630}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-315}=\frac{12}{-630}
=-2/105
$