(N+4)x2=11

Solution for (N+4)x2=11 equation:

(+4)N2=11

We move all terms to the left:

(+4)N2-(11)=0

We add all the numbers together, and all the variables

4N2-11=0

We add all the numbers together, and all the variables

4N^2-11=0

a = 4; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·4·(-11)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{11}}{2*4}=\frac{0-4\sqrt{11}}{8}
=-\frac{4\sqrt{11}}{8}
=-\frac{\sqrt{11}}{2}
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{11}}{2*4}=\frac{0+4\sqrt{11}}{8}
=\frac{4\sqrt{11}}{8}
=\frac{\sqrt{11}}{2}
$