1/2x+1/5x+1/2=19/10

Solution for 1/2x+1/5x+1/2=19/10 equation:

1/2x+1/5x+1/2=19/10

We move all terms to the left:

1/2x+1/5x+1/2-(19/10)=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


We add all the numbers together, and all the variables

1/2x+1/5x+1/2-(+19/10)=0

We get rid of parentheses

1/2x+1/5x+1/2-19/10=0

We calculate fractions


(-1900x^2)/400x^2+50x/400x^2+80x/400x^2+50x/400x^2=0

We multiply all the terms by the denominator


(-1900x^2)+50x+80x+50x=0

We add all the numbers together, and all the variables

(-1900x^2)+180x=0

We get rid of parentheses

-1900x^2+180x=0

a = -1900; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-1900)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*-1900}=\frac{-360}{-3800}
=9/95
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-1900}=\frac{0}{-3800}
=0
$