7/8k+2=1-3/4k

Solution for 7/8k+2=1-3/4k equation:

7/8k+2=1-3/4k

We move all terms to the left:

7/8k+2-(1-3/4k)=0


Domain of the equation: 8k!=0

k!=0/8

k!=0

k∈R



Domain of the equation: 4k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

7/8k-(-3/4k+1)+2=0

We get rid of parentheses

7/8k+3/4k-1+2=0

We calculate fractions


28k/32k^2+24k/32k^2-1+2=0

We add all the numbers together, and all the variables

28k/32k^2+24k/32k^2+1=0

We multiply all the terms by the denominator


28k+24k+1*32k^2=0

We add all the numbers together, and all the variables

52k+1*32k^2=0

Wy multiply elements

32k^2+52k=0

a = 32; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·32·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*32}=\frac{-104}{64}
=-1+5/8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*32}=\frac{0}{64}
=0
$