1/100x+10=-1/150x+30

Solution for 1/100x+10=-1/150x+30 equation:

1/100x+10=-1/150x+30

We move all terms to the left:

1/100x+10-(-1/150x+30)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R



Domain of the equation: 150x+30)!=0

x∈R


We get rid of parentheses

1/100x+1/150x-30+10=0

We calculate fractions


150x/15000x^2+100x/15000x^2-30+10=0

We add all the numbers together, and all the variables

150x/15000x^2+100x/15000x^2-20=0

We multiply all the terms by the denominator


150x+100x-20*15000x^2=0

We add all the numbers together, and all the variables

250x-20*15000x^2=0

Wy multiply elements

-300000x^2+250x=0

a = -300000; b = 250; c = 0;
Δ = b2-4ac
Δ = 2502-4·(-300000)·0
Δ = 62500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{62500}=250$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-250}{2*-300000}=\frac{-500}{-600000}
=1/1200
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+250}{2*-300000}=\frac{0}{-600000}
=0
$