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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


50x^2/200x^2+(-80x)/200x^2+(-20x)/200x^2+1+2=0

We add all the numbers together, and all the variables

50x^2/200x^2+(-80x)/200x^2+(-20x)/200x^2+3=0

We multiply all the terms by the denominator


50x^2+(-80x)+(-20x)+3*200x^2=0

Wy multiply elements

50x^2+600x^2+(-80x)+(-20x)=0

We get rid of parentheses

50x^2+600x^2-80x-20x=0

We add all the numbers together, and all the variables

650x^2-100x=0

a = 650; b = -100; c = 0;
Δ = b2-4ac
Δ = -1002-4·650·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100}{2*650}=\frac{0}{1300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100}{2*650}=\frac{200}{1300}
=2/13
$