3/2x-4/6x=81

Solution for 3/2x-4/6x=81 equation:

3/2x-4/6x=81

We move all terms to the left:

3/2x-4/6x-(81)=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+(-8x)/12x^2-81=0

We multiply all the terms by the denominator


18x+(-8x)-81*12x^2=0

Wy multiply elements

-972x^2+18x+(-8x)=0

We get rid of parentheses

-972x^2+18x-8x=0

We add all the numbers together, and all the variables

-972x^2+10x=0

a = -972; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-972)·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*-972}=\frac{-20}{-1944}
=5/486
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-972}=\frac{0}{-1944}
=0
$