/6x-32=-2x+40

Solution for /6x-32=-2x+40 equation:

/6x-32=-2x+40

We move all terms to the left:

/6x-32-(-2x+40)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

/6x+2x-40-32=0

We multiply all the terms by the denominator


2x*6x-40*6x-32*6x+=0

We add all the numbers together, and all the variables

2x*6x-40*6x-32*6x=0

Wy multiply elements

12x^2-240x-192x=0

We add all the numbers together, and all the variables

12x^2-432x=0

a = 12; b = -432; c = 0;
Δ = b2-4ac
Δ = -4322-4·12·0
Δ = 186624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{186624}=432$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-432)-432}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-432)+432}{2*12}=\frac{864}{24}
=36
$