2/3x+6=0.4x-13

Solution for 2/3x+6=0.4x-13 equation:

2/3x+6=0.4x-13

We move all terms to the left:

2/3x+6-(0.4x-13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-0.4x+13+6=0

We multiply all the terms by the denominator


-(0.4x)*3x+13*3x+6*3x+2=0

We add all the numbers together, and all the variables

-(+0.4x)*3x+13*3x+6*3x+2=0

We multiply parentheses

-0x^2+13*3x+6*3x+2=0

Wy multiply elements

-0x^2+39x+18x+2=0

We add all the numbers together, and all the variables

-1x^2+57x+2=0

a = -1; b = 57; c = +2;
Δ = b2-4ac
Δ = 572-4·(-1)·2
Δ = 3257
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{-(57)-\sqrt{3257}}{2*-1}=\frac{-57-\sqrt{3257}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+\sqrt{3257}}{2*-1}=\frac{-57+\sqrt{3257}}{-2}
$