0.4(x+6)=1/3x+1

Solution for 0.4(x+6)=1/3x+1 equation:

0.4(x+6)=1/3x+1

We move all terms to the left:

0.4(x+6)-(1/3x+1)=0


Domain of the equation: 3x+1)!=0

x∈R


We multiply parentheses

0.4x-(1/3x+1)+2.4=0

We get rid of parentheses

0.4x-1/3x-1+2.4=0

We multiply all the terms by the denominator


(0.4x)*3x-1*3x+(2.4)*3x-1=0

We add all the numbers together, and all the variables

(+0.4x)*3x-1*3x+(2.4)*3x-1=0

We multiply parentheses

0x^2-1*3x+7.2x-1=0

Wy multiply elements

0x^2-3x+7.2x-1=0

We add all the numbers together, and all the variables

x^2+4.2x-1=0

a = 1; b = 4.2; c = -1;
Δ = b2-4ac
Δ = 4.22-4·1·(-1)
Δ = 21.64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4.2)-\sqrt{21.64}}{2*1}=\frac{-4.2-\sqrt{21.64}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.2)+\sqrt{21.64}}{2*1}=\frac{-4.2+\sqrt{21.64}}{2}
$