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

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

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

We move all terms to the left:

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


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x-7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


5x/50x^2+(-10x)/50x^2+7+5=0

We add all the numbers together, and all the variables

5x/50x^2+(-10x)/50x^2+12=0

We multiply all the terms by the denominator


5x+(-10x)+12*50x^2=0

Wy multiply elements

600x^2+5x+(-10x)=0

We get rid of parentheses

600x^2+5x-10x=0

We add all the numbers together, and all the variables

600x^2-5x=0

a = 600; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·600·0
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*600}=\frac{0}{1200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*600}=\frac{10}{1200}
=1/120
$