0.75k+7=1/8k+27

Solution for 0.75k+7=1/8k+27 equation:

0.75k+7=1/8k+27

We move all terms to the left:

0.75k+7-(1/8k+27)=0


Domain of the equation: 8k+27)!=0

k∈R


We get rid of parentheses

0.75k-1/8k-27+7=0

We multiply all the terms by the denominator


(0.75k)*8k-27*8k+7*8k-1=0

We add all the numbers together, and all the variables

(+0.75k)*8k-27*8k+7*8k-1=0

We multiply parentheses

0k^2-27*8k+7*8k-1=0

Wy multiply elements

0k^2-216k+56k-1=0

We add all the numbers together, and all the variables

k^2-160k-1=0

a = 1; b = -160; c = -1;
Δ = b2-4ac
Δ = -1602-4·1·(-1)
Δ = 25604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{25604}=\sqrt{4*6401}=\sqrt{4}*\sqrt{6401}=2\sqrt{6401}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-2\sqrt{6401}}{2*1}=\frac{160-2\sqrt{6401}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+2\sqrt{6401}}{2*1}=\frac{160+2\sqrt{6401}}{2}
$