0.8x=5x/6x-1

Solution for 0.8x=5x/6x-1 equation:

0.8x=5x/6x-1

We move all terms to the left:

0.8x-(5x/6x-1)=0


Domain of the equation: 6x-1)!=0

x∈R


We get rid of parentheses

0.8x-5x/6x+1=0

We multiply all the terms by the denominator


(0.8x)*6x-5x+1*6x=0

We add all the numbers together, and all the variables

(+0.8x)*6x-5x+1*6x=0

We add all the numbers together, and all the variables

-5x+(+0.8x)*6x+1*6x=0

We multiply parentheses

0x^2-5x+1*6x=0

Wy multiply elements

0x^2-5x+6x=0

We add all the numbers together, and all the variables

x^2+x=0

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