3/10x+5/100x=1/10x+2

Solution for 3/10x+5/100x=1/10x+2 equation:

3/10x+5/100x=1/10x+2

We move all terms to the left:

3/10x+5/100x-(1/10x+2)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R



Domain of the equation: 10x+2)!=0

x∈R


We get rid of parentheses

3/10x+5/100x-1/10x-2=0

We calculate fractions


(-100x+3)/1000x^2+50x/1000x^2-2=0

We multiply all the terms by the denominator


(-100x+3)+50x-2*1000x^2=0

We add all the numbers together, and all the variables

50x+(-100x+3)-2*1000x^2=0

Wy multiply elements

-2000x^2+50x+(-100x+3)=0

We get rid of parentheses

-2000x^2+50x-100x+3=0

We add all the numbers together, and all the variables

-2000x^2-50x+3=0

a = -2000; b = -50; c = +3;
Δ = b2-4ac
Δ = -502-4·(-2000)·3
Δ = 26500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{26500}=\sqrt{100*265}=\sqrt{100}*\sqrt{265}=10\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{265}}{2*-2000}=\frac{50-10\sqrt{265}}{-4000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{265}}{2*-2000}=\frac{50+10\sqrt{265}}{-4000}
$