3/4k+10=2-1/8k

Solution for 3/4k+10=2-1/8k equation:

3/4k+10=2-1/8k

We move all terms to the left:

3/4k+10-(2-1/8k)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 8k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

3/4k-(-1/8k+2)+10=0

We get rid of parentheses

3/4k+1/8k-2+10=0

We calculate fractions


24k/32k^2+4k/32k^2-2+10=0

We add all the numbers together, and all the variables

24k/32k^2+4k/32k^2+8=0

We multiply all the terms by the denominator


24k+4k+8*32k^2=0

We add all the numbers together, and all the variables

28k+8*32k^2=0

Wy multiply elements

256k^2+28k=0

a = 256; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·256·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*256}=\frac{-56}{512}
=-7/64
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*256}=\frac{0}{512}
=0
$