n(3n-4)-(7-2n)=0

Solution for n(3n-4)-(7-2n)=0 equation:

n(3n-4)-(7-2n)=0

We add all the numbers together, and all the variables

n(3n-4)-(-2n+7)=0

We multiply parentheses

3n^2-4n-(-2n+7)=0

We get rid of parentheses

3n^2-4n+2n-7=0

We add all the numbers together, and all the variables

3n^2-2n-7=0

a = 3; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·3·(-7)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{22}}{2*3}=\frac{2-2\sqrt{22}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{22}}{2*3}=\frac{2+2\sqrt{22}}{6}
$