4n(2)-3=2n(2)+9

Solution for 4n(2)-3=2n(2)+9 equation:

4n(2)-3=2n(2)+9

We move all terms to the left:

4n(2)-3-(2n(2)+9)=0

We add all the numbers together, and all the variables

-(+2n^2+9)+4n2-3=0

We add all the numbers together, and all the variables

4n^2-(+2n^2+9)-3=0

We get rid of parentheses

4n^2-2n^2-9-3=0

We add all the numbers together, and all the variables

2n^2-12=0

a = 2; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·2·(-12)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*2}=\frac{0-4\sqrt{6}}{4}
=-\frac{4\sqrt{6}}{4}
=-\sqrt{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*2}=\frac{0+4\sqrt{6}}{4}
=\frac{4\sqrt{6}}{4}
=\sqrt{6}
$