74/5k-5/6=7/30k

Solution for 74/5k-5/6=7/30k equation:

74/5k-5/6=7/30k

We move all terms to the left:

74/5k-5/6-(7/30k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 30k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

74/5k-(+7/30k)-5/6=0

We get rid of parentheses

74/5k-7/30k-5/6=0

We calculate fractions


(-2250k^2)/5400k^2+79920k/5400k^2+(-1260k)/5400k^2=0

We multiply all the terms by the denominator


(-2250k^2)+79920k+(-1260k)=0

We get rid of parentheses

-2250k^2+79920k-1260k=0

We add all the numbers together, and all the variables

-2250k^2+78660k=0

a = -2250; b = 78660; c = 0;
Δ = b2-4ac
Δ = 786602-4·(-2250)·0
Δ = 6187395600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6187395600}=78660$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78660)-78660}{2*-2250}=\frac{-157320}{-4500}
=34+24/25
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78660)+78660}{2*-2250}=\frac{0}{-4500}
=0
$