4(1/3x+2)-5/6x=12

Solution for 4(1/3x+2)-5/6x=12 equation:

4(1/3x+2)-5/6x=12

We move all terms to the left:

4(1/3x+2)-5/6x-(12)=0


Domain of the equation: 3x+2)!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply parentheses

4x-5/6x+8-12=0

We multiply all the terms by the denominator


4x*6x+8*6x-12*6x-5=0

Wy multiply elements

24x^2+48x-72x-5=0

We add all the numbers together, and all the variables

24x^2-24x-5=0

a = 24; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·24·(-5)
Δ = 1056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{66}}{2*24}=\frac{24-4\sqrt{66}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{66}}{2*24}=\frac{24+4\sqrt{66}}{48}
$