1+3/5x=7/10x

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Solution for 1+3/5x=7/10x equation: 



1+3/5x=7/10x

We move all terms to the left:

1+3/5x-(7/10x)=0



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R





Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R



We add all the numbers together, and all the variables

3/5x-(+7/10x)+1=0

We get rid of parentheses

3/5x-7/10x+1=0

We calculate fractions


30x/50x^2+(-35x)/50x^2+1=0

We multiply all the terms by the denominator


30x+(-35x)+1*50x^2=0

Wy multiply elements

50x^2+30x+(-35x)=0

We get rid of parentheses

50x^2+30x-35x=0

We add all the numbers together, and all the variables

50x^2-5x=0

a = 50; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·50·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*50}=\frac{0}{100}
=0
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*50}=\frac{10}{100}
=1/10
$

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