3/4k-2/3k=37

Solution for 3/4k-2/3k=37 equation:

3/4k-2/3k=37

We move all terms to the left:

3/4k-2/3k-(37)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R


We calculate fractions


9k/12k^2+(-8k)/12k^2-37=0

We multiply all the terms by the denominator


9k+(-8k)-37*12k^2=0

Wy multiply elements

-444k^2+9k+(-8k)=0

We get rid of parentheses

-444k^2+9k-8k=0

We add all the numbers together, and all the variables

-444k^2+k=0

a = -444; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-444)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-444}=\frac{-2}{-888}
=1/444
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-444}=\frac{0}{-888}
=0
$