4/5x-5/6+7/6x+1/5=1

Solution for 4/5x-5/6+7/6x+1/5=1 equation:

4/5x-5/6+7/6x+1/5=1

We move all terms to the left:

4/5x-5/6+7/6x+1/5-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


determiningTheFunctionDomain
4/5x+7/6x-1-5/6+1/5=0

We calculate fractions


864x/5400x^2+875x/5400x^2+(-625x)/5400x^2+216x/5400x^2-1=0

We multiply all the terms by the denominator


864x+875x+(-625x)+216x-1*5400x^2=0

We add all the numbers together, and all the variables

1955x+(-625x)-1*5400x^2=0

Wy multiply elements

-5400x^2+1955x+(-625x)=0

We get rid of parentheses

-5400x^2+1955x-625x=0

We add all the numbers together, and all the variables

-5400x^2+1330x=0

a = -5400; b = 1330; c = 0;
Δ = b2-4ac
Δ = 13302-4·(-5400)·0
Δ = 1768900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1768900}=1330$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1330)-1330}{2*-5400}=\frac{-2660}{-10800}
=133/540
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1330)+1330}{2*-5400}=\frac{0}{-10800}
=0
$