2n-11=3/2n-8

Solution for 2n-11=3/2n-8 equation:

2n-11=3/2n-8

We move all terms to the left:

2n-11-(3/2n-8)=0


Domain of the equation: 2n-8)!=0

n∈R


We get rid of parentheses

2n-3/2n+8-11=0

We multiply all the terms by the denominator


2n*2n+8*2n-11*2n-3=0

Wy multiply elements

4n^2+16n-22n-3=0

We add all the numbers together, and all the variables

4n^2-6n-3=0

a = 4; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·4·(-3)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*4}=\frac{6-2\sqrt{21}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*4}=\frac{6+2\sqrt{21}}{8}
$