-4k(2k+8)=7(k-6)

Solution for -4k(2k+8)=7(k-6) equation:

-4k(2k+8)=7(k-6)

We move all terms to the left:

-4k(2k+8)-(7(k-6))=0

We multiply parentheses

-8k^2-32k-(7(k-6))=0


We calculate terms in parentheses: -(7(k-6)), so:

7(k-6)

We multiply parentheses

7k-42

Back to the equation:

-(7k-42)


We get rid of parentheses

-8k^2-32k-7k+42=0

We add all the numbers together, and all the variables

-8k^2-39k+42=0

a = -8; b = -39; c = +42;
Δ = b2-4ac
Δ = -392-4·(-8)·42
Δ = 2865
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{-(-39)-\sqrt{2865}}{2*-8}=\frac{39-\sqrt{2865}}{-16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{2865}}{2*-8}=\frac{39+\sqrt{2865}}{-16}
$