n-11=7/n-12=2

Solution for n-11=7/n-12=2 equation:

n-11=7/n-12=2

We move all terms to the left:

n-11-(7/n-12)=0


Domain of the equation: n-12)!=0

n∈R


We get rid of parentheses

n-7/n+12-11=0

We multiply all the terms by the denominator


n*n+12*n-11*n-7=0

We add all the numbers together, and all the variables

n+n*n-7=0

Wy multiply elements

n^2+n-7=0

a = 1; b = 1; c = -7;
Δ = b2-4ac
Δ = 12-4·1·(-7)
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{29}}{2*1}=\frac{-1-\sqrt{29}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{29}}{2*1}=\frac{-1+\sqrt{29}}{2}
$