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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


288x^2/216x^2+54x/216x^2+(-180x)/216x^2+2=0

We multiply all the terms by the denominator


288x^2+54x+(-180x)+2*216x^2=0

Wy multiply elements

288x^2+432x^2+54x+(-180x)=0

We get rid of parentheses

288x^2+432x^2+54x-180x=0

We add all the numbers together, and all the variables

720x^2-126x=0

a = 720; b = -126; c = 0;
Δ = b2-4ac
Δ = -1262-4·720·0
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*720}=\frac{0}{1440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+126}{2*720}=\frac{252}{1440}
=7/40
$