5/6x-8=1/5x+2

Solution for 5/6x-8=1/5x+2 equation:

5/6x-8=1/5x+2

We move all terms to the left:

5/6x-8-(1/5x+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-1/5x-2-8=0

We calculate fractions


25x/30x^2+(-6x)/30x^2-2-8=0

We add all the numbers together, and all the variables

25x/30x^2+(-6x)/30x^2-10=0

We multiply all the terms by the denominator


25x+(-6x)-10*30x^2=0

Wy multiply elements

-300x^2+25x+(-6x)=0

We get rid of parentheses

-300x^2+25x-6x=0

We add all the numbers together, and all the variables

-300x^2+19x=0

a = -300; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-300)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-300}=\frac{-38}{-600}
=19/300
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-300}=\frac{0}{-600}
=0
$