3n*2n=35

Solution for 3n*2n=35 equation:

3n*2n=35

We move all terms to the left:

3n*2n-(35)=0

Wy multiply elements

6n^2-35=0

a = 6; b = 0; c = -35;
Δ = b2-4ac
Δ = 02-4·6·(-35)
Δ = 840
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*6}=\frac{0-2\sqrt{210}}{12}
=-\frac{2\sqrt{210}}{12}
=-\frac{\sqrt{210}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*6}=\frac{0+2\sqrt{210}}{12}
=\frac{2\sqrt{210}}{12}
=\frac{\sqrt{210}}{6}
$