5/2k+1+1/3k-3/4=

Solution for 5/2k+1+1/3k-3/4= equation:

5/2k+1+1/3k-3/4=

We move all terms to the left:

5/2k+1+1/3k-3/4-()=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R


We add all the numbers together, and all the variables

5/2k+1/3k-3/4=0

We calculate fractions


(-54k^2)/96k^2+240k/96k^2+32k/96k^2=0

We multiply all the terms by the denominator


(-54k^2)+240k+32k=0

We add all the numbers together, and all the variables

(-54k^2)+272k=0

We get rid of parentheses

-54k^2+272k=0

a = -54; b = 272; c = 0;
Δ = b2-4ac
Δ = 2722-4·(-54)·0
Δ = 73984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{73984}=272$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(272)-272}{2*-54}=\frac{-544}{-108}
=5+1/27
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(272)+272}{2*-54}=\frac{0}{-108}
=0
$