-3/4k+8/3=-8-7/2k

Solution for -3/4k+8/3=-8-7/2k equation:

-3/4k+8/3=-8-7/2k

We move all terms to the left:

-3/4k+8/3-(-8-7/2k)=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

-3/4k-(-7/2k-8)+8/3=0

We get rid of parentheses

-3/4k+7/2k+8+8/3=0

We calculate fractions


128k^2/72k^2+(-54k)/72k^2+252k/72k^2+8=0

We multiply all the terms by the denominator


128k^2+(-54k)+252k+8*72k^2=0

We add all the numbers together, and all the variables

128k^2+252k+(-54k)+8*72k^2=0

Wy multiply elements

128k^2+576k^2+252k+(-54k)=0

We get rid of parentheses

128k^2+576k^2+252k-54k=0

We add all the numbers together, and all the variables

704k^2+198k=0

a = 704; b = 198; c = 0;
Δ = b2-4ac
Δ = 1982-4·704·0
Δ = 39204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39204}=198$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(198)-198}{2*704}=\frac{-396}{1408}
=-9/32
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(198)+198}{2*704}=\frac{0}{1408}
=0
$