0.8x=5/6x-1

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

0.8x=5/6x-1

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

0.8x-5/6x+1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

Wy multiply elements

0x^2+6x-5=0

We add all the numbers together, and all the variables

x^2+6x-5=0

a = 1; b = 6; c = -5;
Δ = b2-4ac
Δ = 62-4·1·(-5)
Δ = 56
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{14}}{2*1}=\frac{-6-2\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{14}}{2*1}=\frac{-6+2\sqrt{14}}{2}
$