3/2x+4=1/6x-5

Solution for 3/2x+4=1/6x-5 equation:

3/2x+4=1/6x-5

We move all terms to the left:

3/2x+4-(1/6x-5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x-5)!=0

x∈R


We get rid of parentheses

3/2x-1/6x+5+4=0

We calculate fractions


18x/12x^2+(-2x)/12x^2+5+4=0

We add all the numbers together, and all the variables

18x/12x^2+(-2x)/12x^2+9=0

We multiply all the terms by the denominator


18x+(-2x)+9*12x^2=0

Wy multiply elements

108x^2+18x+(-2x)=0

We get rid of parentheses

108x^2+18x-2x=0

We add all the numbers together, and all the variables

108x^2+16x=0

a = 108; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·108·0
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*108}=\frac{-32}{216}
=-4/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*108}=\frac{0}{216}
=0
$