-1/6x+4=5/2x

Solution for -1/6x+4=5/2x equation:

-1/6x+4=5/2x

We move all terms to the left:

-1/6x+4-(5/2x)=0


Domain of the equation: 6x!=0

x!=0/6

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

-1/6x-(+5/2x)+4=0

We get rid of parentheses

-1/6x-5/2x+4=0

We calculate fractions


(-2x)/12x^2+(-30x)/12x^2+4=0

We multiply all the terms by the denominator


(-2x)+(-30x)+4*12x^2=0

Wy multiply elements

48x^2+(-2x)+(-30x)=0

We get rid of parentheses

48x^2-2x-30x=0

We add all the numbers together, and all the variables

48x^2-32x=0

a = 48; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·48·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*48}=\frac{0}{96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*48}=\frac{64}{96}
=2/3
$