2/3+1/5x=5/6,x=

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

2/3+1/5x=5/6.x=

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6.x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


360x^2/90x^2+18x/90x^2+(-225x)/90x^2=0

We multiply all the terms by the denominator


360x^2+18x+(-225x)=0

We get rid of parentheses

360x^2+18x-225x=0

We add all the numbers together, and all the variables

360x^2-207x=0

a = 360; b = -207; c = 0;
Δ = b2-4ac
Δ = -2072-4·360·0
Δ = 42849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{42849}=207$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-207)-207}{2*360}=\frac{0}{720}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-207)+207}{2*360}=\frac{414}{720}
=23/40
$