1/4k=-0.75k+9

Solution for 1/4k=-0.75k+9 equation:

1/4k=-0.75k+9

We move all terms to the left:

1/4k-(-0.75k+9)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R


We get rid of parentheses

1/4k+0.75k-9=0

We multiply all the terms by the denominator


(0.75k)*4k-9*4k+1=0

We add all the numbers together, and all the variables

(+0.75k)*4k-9*4k+1=0

We multiply parentheses

0k^2-9*4k+1=0

Wy multiply elements

0k^2-36k+1=0

We add all the numbers together, and all the variables

k^2-36k+1=0

a = 1; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·1·1
Δ = 1292
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:

$\sqrt{\Delta}=\sqrt{1292}=\sqrt{4*323}=\sqrt{4}*\sqrt{323}=2\sqrt{323}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{323}}{2*1}=\frac{36-2\sqrt{323}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{323}}{2*1}=\frac{36+2\sqrt{323}}{2}
$