n2+13/11=12-5

Solution for n2+13/11=12-5 equation:

n2+13/11=12-5

We move all terms to the left:

n2+13/11-(12-5)=0

We add all the numbers together, and all the variables

n2+13/11-7=0

We add all the numbers together, and all the variables

n^2-7+13/11=0

We multiply all the terms by the denominator


n^2*11+13-7*11=0

We add all the numbers together, and all the variables

n^2*11-64=0

Wy multiply elements

11n^2-64=0

a = 11; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·11·(-64)
Δ = 2816
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:

$\sqrt{\Delta}=\sqrt{2816}=\sqrt{256*11}=\sqrt{256}*\sqrt{11}=16\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{11}}{2*11}=\frac{0-16\sqrt{11}}{22}
=-\frac{16\sqrt{11}}{22}
=-\frac{8\sqrt{11}}{11}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{11}}{2*11}=\frac{0+16\sqrt{11}}{22}
=\frac{16\sqrt{11}}{22}
=\frac{8\sqrt{11}}{11}
$