5x/2=1-x/6,xER

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

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

We move all terms to the left:

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


Domain of the equation: 6.x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


30x^2/12x+2x/12x-1=0

We multiply all the terms by the denominator


30x^2+2x-1*12x=0

Wy multiply elements

30x^2+2x-12x=0

We add all the numbers together, and all the variables

30x^2-10x=0

a = 30; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·30·0
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*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*30}=\frac{20}{60}
=1/3
$