1/2x-1/5x+1/10=2

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

1/2x-1/5x+1/10=2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


determiningTheFunctionDomain
1/2x-1/5x-2+1/10=0

We calculate fractions


50x^2/100x^2+50x/100x^2+(-20x)/100x^2-2=0

We multiply all the terms by the denominator


50x^2+50x+(-20x)-2*100x^2=0

Wy multiply elements

50x^2-200x^2+50x+(-20x)=0

We get rid of parentheses

50x^2-200x^2+50x-20x=0

We add all the numbers together, and all the variables

-150x^2+30x=0

a = -150; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-150)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-150}=\frac{-60}{-300}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-150}=\frac{0}{-300}
=0
$