11/4k-3/8k=28

Solution for 11/4k-3/8k=28 equation:

11/4k-3/8k=28

We move all terms to the left:

11/4k-3/8k-(28)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 8k!=0

k!=0/8

k!=0

k∈R


We calculate fractions


88k/32k^2+(-12k)/32k^2-28=0

We multiply all the terms by the denominator


88k+(-12k)-28*32k^2=0

Wy multiply elements

-896k^2+88k+(-12k)=0

We get rid of parentheses

-896k^2+88k-12k=0

We add all the numbers together, and all the variables

-896k^2+76k=0

a = -896; b = 76; c = 0;
Δ = b2-4ac
Δ = 762-4·(-896)·0
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-76}{2*-896}=\frac{-152}{-1792}
=19/224
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+76}{2*-896}=\frac{0}{-1792}
=0
$