2/3x-5/6=-5/12x+4

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

2/3x-5/6=-5/12x+4

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


(-180x^2)/1296x^2+864x/1296x^2+540x/1296x^2-4=0

We multiply all the terms by the denominator


(-180x^2)+864x+540x-4*1296x^2=0

We add all the numbers together, and all the variables

(-180x^2)+1404x-4*1296x^2=0

Wy multiply elements

(-180x^2)-5184x^2+1404x=0

We get rid of parentheses

-180x^2-5184x^2+1404x=0

We add all the numbers together, and all the variables

-5364x^2+1404x=0

a = -5364; b = 1404; c = 0;
Δ = b2-4ac
Δ = 14042-4·(-5364)·0
Δ = 1971216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1971216}=1404$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1404)-1404}{2*-5364}=\frac{-2808}{-10728}
=39/149
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1404)+1404}{2*-5364}=\frac{0}{-10728}
=0
$