1/5x+4=0.6x+8

Solution for 1/5x+4=0.6x+8 equation:

1/5x+4=0.6x+8

We move all terms to the left:

1/5x+4-(0.6x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-0.6x-8+4=0

We multiply all the terms by the denominator


-(0.6x)*5x-8*5x+4*5x+1=0

We add all the numbers together, and all the variables

-(+0.6x)*5x-8*5x+4*5x+1=0

We multiply parentheses

-0x^2-8*5x+4*5x+1=0

Wy multiply elements

-0x^2-40x+20x+1=0

We add all the numbers together, and all the variables

-1x^2-20x+1=0

a = -1; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·(-1)·1
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{101}}{2*-1}=\frac{20-2\sqrt{101}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{101}}{2*-1}=\frac{20+2\sqrt{101}}{-2}
$