4n+7=n2

Solution for 4n+7=n2 equation:

4n+7=n2

We move all terms to the left:

4n+7-(n2)=0

We add all the numbers together, and all the variables

-1n^2+4n+7=0

a = -1; b = 4; c = +7;
Δ = b2-4ac
Δ = 42-4·(-1)·7
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{11}}{2*-1}=\frac{-4-2\sqrt{11}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{11}}{2*-1}=\frac{-4+2\sqrt{11}}{-2}
$