3n^2+6n=75

Solution for 3n^2+6n=75 equation:

3n^2+6n=75

We move all terms to the left:

3n^2+6n-(75)=0

a = 3; b = 6; c = -75;
Δ = b2-4ac
Δ = 62-4·3·(-75)
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{26}}{2*3}=\frac{-6-6\sqrt{26}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{26}}{2*3}=\frac{-6+6\sqrt{26}}{6}
$