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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


288x^2/96x^2+16x/96x^2+(-24x)/96x^2+5=0

We multiply all the terms by the denominator


288x^2+16x+(-24x)+5*96x^2=0

Wy multiply elements

288x^2+480x^2+16x+(-24x)=0

We get rid of parentheses

288x^2+480x^2+16x-24x=0

We add all the numbers together, and all the variables

768x^2-8x=0

a = 768; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·768·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*768}=\frac{0}{1536}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*768}=\frac{16}{1536}
=1/96
$