-7/8k=-21k=24

Solution for -7/8k=-21k=24 equation:

-7/8k=-21k=24

We move all terms to the left:

-7/8k-(-21k)=0


Domain of the equation: 8k!=0

k!=0/8

k!=0

k∈R


We get rid of parentheses

-7/8k+21k=0

We multiply all the terms by the denominator


21k*8k-7=0

Wy multiply elements

168k^2-7=0

a = 168; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·168·(-7)
Δ = 4704
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:

$\sqrt{\Delta}=\sqrt{4704}=\sqrt{784*6}=\sqrt{784}*\sqrt{6}=28\sqrt{6}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{6}}{2*168}=\frac{0-28\sqrt{6}}{336}
=-\frac{28\sqrt{6}}{336}
=-\frac{\sqrt{6}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{6}}{2*168}=\frac{0+28\sqrt{6}}{336}
=\frac{28\sqrt{6}}{336}
=\frac{\sqrt{6}}{12}
$