(7/8)k=5/6

Solution for (7/8)k=5/6 equation:

(7/8)k=5/6

We move all terms to the left:

(7/8)k-(5/6)=0


Domain of the equation: 8)k!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

(+7/8)k-(+5/6)=0

We multiply parentheses

7k^2-(+5/6)=0

We get rid of parentheses

7k^2-5/6=0

We multiply all the terms by the denominator


7k^2*6-5=0

Wy multiply elements

42k^2-5=0

a = 42; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·42·(-5)
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*42}=\frac{0-2\sqrt{210}}{84}
=-\frac{2\sqrt{210}}{84}
=-\frac{\sqrt{210}}{42}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*42}=\frac{0+2\sqrt{210}}{84}
=\frac{2\sqrt{210}}{84}
=\frac{\sqrt{210}}{42}
$