4+n-9=-9/2n-12

Solution for 4+n-9=-9/2n-12 equation:

4+n-9=-9/2n-12

We move all terms to the left:

4+n-9-(-9/2n-12)=0


Domain of the equation: 2n-12)!=0

n∈R


We add all the numbers together, and all the variables

n-(-9/2n-12)-5=0

We get rid of parentheses

n+9/2n+12-5=0

We multiply all the terms by the denominator


n*2n+12*2n-5*2n+9=0

Wy multiply elements

2n^2+24n-10n+9=0

We add all the numbers together, and all the variables

2n^2+14n+9=0

a = 2; b = 14; c = +9;
Δ = b2-4ac
Δ = 142-4·2·9
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{31}}{2*2}=\frac{-14-2\sqrt{31}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{31}}{2*2}=\frac{-14+2\sqrt{31}}{4}
$