2.4k(2k-8)+17=27k

Solution for 2.4k(2k-8)+17=27k equation:

2.4k(2k-8)+17=27k

We move all terms to the left:

2.4k(2k-8)+17-(27k)=0

We add all the numbers together, and all the variables

-27k+2.4k(2k-8)+17=0

We multiply parentheses

4k^2-27k-16k+17=0

We add all the numbers together, and all the variables

4k^2-43k+17=0

a = 4; b = -43; c = +17;
Δ = b2-4ac
Δ = -432-4·4·17
Δ = 1577
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-\sqrt{1577}}{2*4}=\frac{43-\sqrt{1577}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+\sqrt{1577}}{2*4}=\frac{43+\sqrt{1577}}{8}
$