5/2k+1-14/3k=-5/8

Solution for 5/2k+1-14/3k=-5/8 equation:

5/2k+1-14/3k=-5/8

We move all terms to the left:

5/2k+1-14/3k-(-5/8)=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 get rid of parentheses

5/2k-14/3k+1+5/8=0

We calculate fractions


90k^2/384k^2+960k/384k^2+(-1792k)/384k^2+1=0

We multiply all the terms by the denominator


90k^2+960k+(-1792k)+1*384k^2=0

Wy multiply elements

90k^2+384k^2+960k+(-1792k)=0

We get rid of parentheses

90k^2+384k^2+960k-1792k=0

We add all the numbers together, and all the variables

474k^2-832k=0

a = 474; b = -832; c = 0;
Δ = b2-4ac
Δ = -8322-4·474·0
Δ = 692224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{692224}=832$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-832)-832}{2*474}=\frac{0}{948}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-832)+832}{2*474}=\frac{1664}{948}
=1+179/237
$