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

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

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

We move all terms to the left:

-3/2x-1/6x-(-1/4)=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 get rid of parentheses

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

We calculate fractions


72x^2/192x^2+(-288x)/192x^2+(-32x)/192x^2=0

We multiply all the terms by the denominator


72x^2+(-288x)+(-32x)=0

We get rid of parentheses

72x^2-288x-32x=0

We add all the numbers together, and all the variables

72x^2-320x=0

a = 72; b = -320; c = 0;
Δ = b2-4ac
Δ = -3202-4·72·0
Δ = 102400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{102400}=320$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-320}{2*72}=\frac{0}{144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+320}{2*72}=\frac{640}{144}
=4+4/9
$