2/5x-3=6-1/2x

Solution for 2/5x-3=6-1/2x equation:

2/5x-3=6-1/2x

We move all terms to the left:

2/5x-3-(6-1/2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-(-1/2x+6)-3=0

We get rid of parentheses

2/5x+1/2x-6-3=0

We calculate fractions


4x/10x^2+5x/10x^2-6-3=0

We add all the numbers together, and all the variables

4x/10x^2+5x/10x^2-9=0

We multiply all the terms by the denominator


4x+5x-9*10x^2=0

We add all the numbers together, and all the variables

9x-9*10x^2=0

Wy multiply elements

-90x^2+9x=0

a = -90; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-90)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-90}=\frac{-18}{-180}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-90}=\frac{0}{-180}
=0
$