u(u+6)=3

Solution for u(u+6)=3 equation:

u(u+6)=3

We move all terms to the left:

u(u+6)-(3)=0

We multiply parentheses

u^2+6u-3=0

a = 1; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·1·(-3)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{3}}{2*1}=\frac{-6-4\sqrt{3}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{3}}{2*1}=\frac{-6+4\sqrt{3}}{2}
$