1.5-0.4k+3=5-1/3k

Solution for 1.5-0.4k+3=5-1/3k equation:

1.5-0.4k+3=5-1/3k

We move all terms to the left:

1.5-0.4k+3-(5-1/3k)=0


Domain of the equation: 3k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-0.4k-(-1/3k+5)+1.5+3=0

We add all the numbers together, and all the variables

-0.4k-(-1/3k+5)+4.5=0

We get rid of parentheses

-0.4k+1/3k-5+4.5=0

We multiply all the terms by the denominator


-(0.4k)*3k-5*3k+(4.5)*3k+1=0

We add all the numbers together, and all the variables

-(+0.4k)*3k-5*3k+(4.5)*3k+1=0

We multiply parentheses

-0k^2-5*3k+13.5k+1=0

Wy multiply elements

-0k^2-15k+13.5k+1=0

We add all the numbers together, and all the variables

-1k^2-1.5k+1=0

a = -1; b = -1.5; c = +1;
Δ = b2-4ac
Δ = -1.52-4·(-1)·1
Δ = 6.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.5)-\sqrt{6.25}}{2*-1}=\frac{1.5-\sqrt{6.25}}{-2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{6.25}}{2*-1}=\frac{1.5+\sqrt{6.25}}{-2}
$