3n^2+6n=46=4

Solution for 3n^2+6n=46=4 equation:

3n^2+6n=46=4

We move all terms to the left:

3n^2+6n-(46)=0

a = 3; b = 6; c = -46;
Δ = b2-4ac
Δ = 62-4·3·(-46)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14\sqrt{3}}{2*3}=\frac{-6-14\sqrt{3}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14\sqrt{3}}{2*3}=\frac{-6+14\sqrt{3}}{6}
$