5/6x+2/3=1/4x-3

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

5/6x+2/3=1/4x-3

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


192x^2/216x^2+180x/216x^2+(-54x)/216x^2+3=0

We multiply all the terms by the denominator


192x^2+180x+(-54x)+3*216x^2=0

Wy multiply elements

192x^2+648x^2+180x+(-54x)=0

We get rid of parentheses

192x^2+648x^2+180x-54x=0

We add all the numbers together, and all the variables

840x^2+126x=0

a = 840; b = 126; c = 0;
Δ = b2-4ac
Δ = 1262-4·840·0
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-126}{2*840}=\frac{-252}{1680}
=-3/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+126}{2*840}=\frac{0}{1680}
=0
$