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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


20x^2/100x^2+40x/100x^2+(-50x)/100x^2-2=0

We multiply all the terms by the denominator


20x^2+40x+(-50x)-2*100x^2=0

Wy multiply elements

20x^2-200x^2+40x+(-50x)=0

We get rid of parentheses

20x^2-200x^2+40x-50x=0

We add all the numbers together, and all the variables

-180x^2-10x=0

a = -180; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-180)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-180}=\frac{0}{-360}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-180}=\frac{20}{-360}
=-1/18
$