3/5k-5=7/100k

Solution for 3/5k-5=7/100k equation:

3/5k-5=7/100k

We move all terms to the left:

3/5k-5-(7/100k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 100k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

3/5k-(+7/100k)-5=0

We get rid of parentheses

3/5k-7/100k-5=0

We calculate fractions


300k/500k^2+(-35k)/500k^2-5=0

We multiply all the terms by the denominator


300k+(-35k)-5*500k^2=0

Wy multiply elements

-2500k^2+300k+(-35k)=0

We get rid of parentheses

-2500k^2+300k-35k=0

We add all the numbers together, and all the variables

-2500k^2+265k=0

a = -2500; b = 265; c = 0;
Δ = b2-4ac
Δ = 2652-4·(-2500)·0
Δ = 70225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{70225}=265$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(265)-265}{2*-2500}=\frac{-530}{-5000}
=53/500
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(265)+265}{2*-2500}=\frac{0}{-5000}
=0
$