5n*7n=35n

Solution for 5n*7n=35n equation:

5n*7n=35n

We move all terms to the left:

5n*7n-(35n)=0

We add all the numbers together, and all the variables

-35n+5n*7n=0

Wy multiply elements

35n^2-35n=0

a = 35; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·35·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*35}=\frac{0}{70}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*35}=\frac{70}{70}
=1
$