5-5/3k=1+k

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

5-5/3k=1+k

We move all terms to the left:

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


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-k*3k-1*3k+5*3k-5=0

Wy multiply elements

-3k^2-3k+15k-5=0

We add all the numbers together, and all the variables

-3k^2+12k-5=0

a = -3; b = 12; c = -5;
Δ = b2-4ac
Δ = 122-4·(-3)·(-5)
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{21}}{2*-3}=\frac{-12-2\sqrt{21}}{-6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{21}}{2*-3}=\frac{-12+2\sqrt{21}}{-6}
$