-7/4k-5/6=3+3/2k

Solution for -7/4k-5/6=3+3/2k equation:

-7/4k-5/6=3+3/2k

We move all terms to the left:

-7/4k-5/6-(3+3/2k)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 2k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-7/4k-(3/2k+3)-5/6=0

We get rid of parentheses

-7/4k-3/2k-3-5/6=0

We calculate fractions


(-80k^2)/288k^2+(-504k)/288k^2+(-432k)/288k^2-3=0

We multiply all the terms by the denominator


(-80k^2)+(-504k)+(-432k)-3*288k^2=0

Wy multiply elements

(-80k^2)-864k^2+(-504k)+(-432k)=0

We get rid of parentheses

-80k^2-864k^2-504k-432k=0

We add all the numbers together, and all the variables

-944k^2-936k=0

a = -944; b = -936; c = 0;
Δ = b2-4ac
Δ = -9362-4·(-944)·0
Δ = 876096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{876096}=936$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-936)-936}{2*-944}=\frac{0}{-1888}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-936)+936}{2*-944}=\frac{1872}{-1888}
=-117/118
$