3u*5u=16

Solution for 3u*5u=16 equation:

3u*5u=16

We move all terms to the left:

3u*5u-(16)=0

Wy multiply elements

15u^2-16=0

a = 15; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·15·(-16)
Δ = 960
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*15}=\frac{0-8\sqrt{15}}{30}
=-\frac{8\sqrt{15}}{30}
=-\frac{4\sqrt{15}}{15}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*15}=\frac{0+8\sqrt{15}}{30}
=\frac{8\sqrt{15}}{30}
=\frac{4\sqrt{15}}{15}
$