1/4x-5/6x=211/12

Solution for 1/4x-5/6x=211/12 equation:

1/4x-5/6x=211/12

We move all terms to the left:

1/4x-5/6x-(211/12)=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-5/6x-(+211/12)=0

We get rid of parentheses

1/4x-5/6x-211/12=0

We calculate fractions


(-30384x^2)/288x^2+72x/288x^2+(-240x)/288x^2=0

We multiply all the terms by the denominator


(-30384x^2)+72x+(-240x)=0

We get rid of parentheses

-30384x^2+72x-240x=0

We add all the numbers together, and all the variables

-30384x^2-168x=0

a = -30384; b = -168; c = 0;
Δ = b2-4ac
Δ = -1682-4·(-30384)·0
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-168}{2*-30384}=\frac{0}{-60768}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+168}{2*-30384}=\frac{336}{-60768}
=-7/1266
$