3/2x-1/6x=5

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

3/2x-1/6x=5

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


18x/12x^2+(-2x)/12x^2-5=0

We multiply all the terms by the denominator


18x+(-2x)-5*12x^2=0

Wy multiply elements

-60x^2+18x+(-2x)=0

We get rid of parentheses

-60x^2+18x-2x=0

We add all the numbers together, and all the variables

-60x^2+16x=0

a = -60; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-60)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-60}=\frac{-32}{-120}
=4/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-60}=\frac{0}{-120}
=0
$