2/7^s+5/6^s=21

Solution for 2/7^s+5/6^s=21 equation:

2/7^s+5/6^s=21

We move all terms to the left:

2/7^s+5/6^s-(21)=0


Domain of the equation: 7^s!=0

s!=0/1

s!=0

s∈R



Domain of the equation: 6^s!=0

s!=0/1

s!=0

s∈R


We calculate fractions


12s/42s^2+35s/42s^2-21=0

We multiply all the terms by the denominator


12s+35s-21*42s^2=0

We add all the numbers together, and all the variables

47s-21*42s^2=0

Wy multiply elements

-882s^2+47s=0

a = -882; b = 47; c = 0;
Δ = b2-4ac
Δ = 472-4·(-882)·0
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-47}{2*-882}=\frac{-94}{-1764}
=47/882
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+47}{2*-882}=\frac{0}{-1764}
=0
$