5k+7=3/8k+81

Solution for 5k+7=3/8k+81 equation:

5k+7=3/8k+81

We move all terms to the left:

5k+7-(3/8k+81)=0


Domain of the equation: 8k+81)!=0

k∈R


We get rid of parentheses

5k-3/8k-81+7=0

We multiply all the terms by the denominator


5k*8k-81*8k+7*8k-3=0

Wy multiply elements

40k^2-648k+56k-3=0

We add all the numbers together, and all the variables

40k^2-592k-3=0

a = 40; b = -592; c = -3;
Δ = b2-4ac
Δ = -5922-4·40·(-3)
Δ = 350944
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:

$\sqrt{\Delta}=\sqrt{350944}=\sqrt{16*21934}=\sqrt{16}*\sqrt{21934}=4\sqrt{21934}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-592)-4\sqrt{21934}}{2*40}=\frac{592-4\sqrt{21934}}{80}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-592)+4\sqrt{21934}}{2*40}=\frac{592+4\sqrt{21934}}{80}
$