5/12x-2/3=2+3/4x

Solution for 5/12x-2/3=2+3/4x equation:

5/12x-2/3=2+3/4x

We move all terms to the left:

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


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5/12x-3/4x-2-2/3=0

We calculate fractions


(-384x^2)/432x^2+180x/432x^2+(-324x)/432x^2-2=0

We multiply all the terms by the denominator


(-384x^2)+180x+(-324x)-2*432x^2=0

Wy multiply elements

(-384x^2)-864x^2+180x+(-324x)=0

We get rid of parentheses

-384x^2-864x^2+180x-324x=0

We add all the numbers together, and all the variables

-1248x^2-144x=0

a = -1248; b = -144; c = 0;
Δ = b2-4ac
Δ = -1442-4·(-1248)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-144}{2*-1248}=\frac{0}{-2496}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+144}{2*-1248}=\frac{288}{-2496}
=-3/26
$