1/3x+0.6x=42

Solution for 1/3x+0.6x=42 equation:

1/3x+0.6x=42

We move all terms to the left:

1/3x+0.6x-(42)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

0.6x+1/3x-42=0

We multiply all the terms by the denominator


(0.6x)*3x-42*3x+1=0

We add all the numbers together, and all the variables

(+0.6x)*3x-42*3x+1=0

We multiply parentheses

0x^2-42*3x+1=0

Wy multiply elements

0x^2-126x+1=0

We add all the numbers together, and all the variables

x^2-126x+1=0

a = 1; b = -126; c = +1;
Δ = b2-4ac
Δ = -1262-4·1·1
Δ = 15872
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:

$\sqrt{\Delta}=\sqrt{15872}=\sqrt{256*62}=\sqrt{256}*\sqrt{62}=16\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-16\sqrt{62}}{2*1}=\frac{126-16\sqrt{62}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+16\sqrt{62}}{2*1}=\frac{126+16\sqrt{62}}{2}
$