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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 5x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


25x/30x^2+(-24x)/30x^2+2+2=0

We add all the numbers together, and all the variables

25x/30x^2+(-24x)/30x^2+4=0

We multiply all the terms by the denominator


25x+(-24x)+4*30x^2=0

Wy multiply elements

120x^2+25x+(-24x)=0

We get rid of parentheses

120x^2+25x-24x=0

We add all the numbers together, and all the variables

120x^2+x=0

a = 120; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·120·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*120}=\frac{-2}{240}
=-1/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*120}=\frac{0}{240}
=0
$