1/5x-1/2=5-3/10x

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

1/5x-1/2=5-3/10x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-50x^2)/200x^2+40x/200x^2+60x/200x^2-5=0

We multiply all the terms by the denominator


(-50x^2)+40x+60x-5*200x^2=0

We add all the numbers together, and all the variables

(-50x^2)+100x-5*200x^2=0

Wy multiply elements

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

We get rid of parentheses

-50x^2-1000x^2+100x=0

We add all the numbers together, and all the variables

-1050x^2+100x=0

a = -1050; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·(-1050)·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*-1050}=\frac{-200}{-2100}
=2/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*-1050}=\frac{0}{-2100}
=0
$