1/5x-3/10=1/100x+5

Solution for 1/5x-3/10=1/100x+5 equation:

1/5x-3/10=1/100x+5

We move all terms to the left:

1/5x-3/10-(1/100x+5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 100x+5)!=0

x∈R


We get rid of parentheses

1/5x-1/100x-5-3/10=0

We calculate fractions


(-1500x^2)/5000x^2+1000x/5000x^2+(-50x)/5000x^2-5=0

We multiply all the terms by the denominator


(-1500x^2)+1000x+(-50x)-5*5000x^2=0

Wy multiply elements

(-1500x^2)-25000x^2+1000x+(-50x)=0

We get rid of parentheses

-1500x^2-25000x^2+1000x-50x=0

We add all the numbers together, and all the variables

-26500x^2+950x=0

a = -26500; b = 950; c = 0;
Δ = b2-4ac
Δ = 9502-4·(-26500)·0
Δ = 902500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{902500}=950$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(950)-950}{2*-26500}=\frac{-1900}{-53000}
=19/530
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(950)+950}{2*-26500}=\frac{0}{-53000}
=0
$