1/4x+3/6x=5/12

Solution for 1/4x+3/6x=5/12 equation:

1/4x+3/6x=5/12

We move all terms to the left:

1/4x+3/6x-(5/12)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x+3/6x-(+5/12)=0

We get rid of parentheses

1/4x+3/6x-5/12=0

We calculate fractions


(-720x^2)/288x^2+72x/288x^2+144x/288x^2=0

We multiply all the terms by the denominator


(-720x^2)+72x+144x=0

We add all the numbers together, and all the variables

(-720x^2)+216x=0

We get rid of parentheses

-720x^2+216x=0

a = -720; b = 216; c = 0;
Δ = b2-4ac
Δ = 2162-4·(-720)·0
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-216}{2*-720}=\frac{-432}{-1440}
=3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+216}{2*-720}=\frac{0}{-1440}
=0
$