2/5x+2/3=5/6x

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

2/5x+2/3=5/6x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


360x^2/270x^2+108x/270x^2+(-225x)/270x^2=0

We multiply all the terms by the denominator


360x^2+108x+(-225x)=0

We get rid of parentheses

360x^2+108x-225x=0

We add all the numbers together, and all the variables

360x^2-117x=0

a = 360; b = -117; c = 0;
Δ = b2-4ac
Δ = -1172-4·360·0
Δ = 13689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13689}=117$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-117)-117}{2*360}=\frac{0}{720}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+117}{2*360}=\frac{234}{720}
=13/40
$