5k+7=3/8k+24

Solution for 5k+7=3/8k+24 equation:

5k+7=3/8k+24

We move all terms to the left:

5k+7-(3/8k+24)=0


Domain of the equation: 8k+24)!=0

k∈R


We get rid of parentheses

5k-3/8k-24+7=0

We multiply all the terms by the denominator


5k*8k-24*8k+7*8k-3=0

Wy multiply elements

40k^2-192k+56k-3=0

We add all the numbers together, and all the variables

40k^2-136k-3=0

a = 40; b = -136; c = -3;
Δ = b2-4ac
Δ = -1362-4·40·(-3)
Δ = 18976
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:

$\sqrt{\Delta}=\sqrt{18976}=\sqrt{16*1186}=\sqrt{16}*\sqrt{1186}=4\sqrt{1186}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-136)-4\sqrt{1186}}{2*40}=\frac{136-4\sqrt{1186}}{80}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-136)+4\sqrt{1186}}{2*40}=\frac{136+4\sqrt{1186}}{80}
$