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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-50x^2)/200x^2+80x/200x^2+(-60x)/200x^2-3=0

We multiply all the terms by the denominator


(-50x^2)+80x+(-60x)-3*200x^2=0

Wy multiply elements

(-50x^2)-600x^2+80x+(-60x)=0

We get rid of parentheses

-50x^2-600x^2+80x-60x=0

We add all the numbers together, and all the variables

-650x^2+20x=0

a = -650; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-650)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-650}=\frac{-40}{-1300}
=2/65
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-650}=\frac{0}{-1300}
=0
$