5/6x+3=4/5x-8+1

Solution for 5/6x+3=4/5x-8+1 equation:

5/6x+3=4/5x-8+1

We move all terms to the left:

5/6x+3-(4/5x-8+1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 5x-8+1)!=0

We move all terms containing x to the left, all other terms to the right

5x+1)!=8

x∈R


We add all the numbers together, and all the variables

5/6x-(4/5x-7)+3=0

We get rid of parentheses

5/6x-4/5x+7+3=0

We calculate fractions


25x/30x^2+(-24x)/30x^2+7+3=0

We add all the numbers together, and all the variables

25x/30x^2+(-24x)/30x^2+10=0

We multiply all the terms by the denominator


25x+(-24x)+10*30x^2=0

Wy multiply elements

300x^2+25x+(-24x)=0

We get rid of parentheses

300x^2+25x-24x=0

We add all the numbers together, and all the variables

300x^2+x=0

a = 300; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·300·0
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*300}=\frac{-2}{600}
=-1/300
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*300}=\frac{0}{600}
=0
$