5-3/5k=1+k

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

5-3/5k=1+k

We move all terms to the left:

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


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-5k^2-5k+25k-3=0

We add all the numbers together, and all the variables

-5k^2+20k-3=0

a = -5; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·(-5)·(-3)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{85}}{2*-5}=\frac{-20-2\sqrt{85}}{-10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{85}}{2*-5}=\frac{-20+2\sqrt{85}}{-10}
$