4/5x-7=1/10x

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

4/5x-7=1/10x

We move all terms to the left:

4/5x-7-(1/10x)=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

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

We get rid of parentheses

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

We calculate fractions


40x/50x^2+(-5x)/50x^2-7=0

We multiply all the terms by the denominator


40x+(-5x)-7*50x^2=0

Wy multiply elements

-350x^2+40x+(-5x)=0

We get rid of parentheses

-350x^2+40x-5x=0

We add all the numbers together, and all the variables

-350x^2+35x=0

a = -350; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·(-350)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*-350}=\frac{-70}{-700}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*-350}=\frac{0}{-700}
=0
$