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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x+12)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


20x/24x^2+(-18x)/24x^2-12+4=0

We add all the numbers together, and all the variables

20x/24x^2+(-18x)/24x^2-8=0

We multiply all the terms by the denominator


20x+(-18x)-8*24x^2=0

Wy multiply elements

-192x^2+20x+(-18x)=0

We get rid of parentheses

-192x^2+20x-18x=0

We add all the numbers together, and all the variables

-192x^2+2x=0

a = -192; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-192)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-192}=\frac{-4}{-384}
=1/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-192}=\frac{0}{-384}
=0
$