3n^2+4n+7=5n^2

Solution for 3n^2+4n+7=5n^2 equation:

3n^2+4n+7=5n^2

We move all terms to the left:

3n^2+4n+7-(5n^2)=0

determiningTheFunctionDomain
3n^2-5n^2+4n+7=0

We add all the numbers together, and all the variables

-2n^2+4n+7=0

a = -2; b = 4; c = +7;
Δ = b2-4ac
Δ = 42-4·(-2)·7
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{2}}{2*-2}=\frac{-4-6\sqrt{2}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{2}}{2*-2}=\frac{-4+6\sqrt{2}}{-4}
$