3/4k-1/3=4+6/5k

Solution for 3/4k-1/3=4+6/5k equation:

3/4k-1/3=4+6/5k

We move all terms to the left:

3/4k-1/3-(4+6/5k)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 5k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

3/4k-(6/5k+4)-1/3=0

We get rid of parentheses

3/4k-6/5k-4-1/3=0

We calculate fractions


(-100k^2)/180k^2+135k/180k^2+(-216k)/180k^2-4=0

We multiply all the terms by the denominator


(-100k^2)+135k+(-216k)-4*180k^2=0

Wy multiply elements

(-100k^2)-720k^2+135k+(-216k)=0

We get rid of parentheses

-100k^2-720k^2+135k-216k=0

We add all the numbers together, and all the variables

-820k^2-81k=0

a = -820; b = -81; c = 0;
Δ = b2-4ac
Δ = -812-4·(-820)·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-81}{2*-820}=\frac{0}{-1640}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+81}{2*-820}=\frac{162}{-1640}
=-81/820
$