-4n(n-2)=5-3n

Solution for -4n(n-2)=5-3n equation:

-4n(n-2)=5-3n

We move all terms to the left:

-4n(n-2)-(5-3n)=0

We add all the numbers together, and all the variables

-4n(n-2)-(-3n+5)=0

We multiply parentheses

-4n^2+8n-(-3n+5)=0

We get rid of parentheses

-4n^2+8n+3n-5=0

We add all the numbers together, and all the variables

-4n^2+11n-5=0

a = -4; b = 11; c = -5;
Δ = b2-4ac
Δ = 112-4·(-4)·(-5)
Δ = 41
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{-(11)-\sqrt{41}}{2*-4}=\frac{-11-\sqrt{41}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{41}}{2*-4}=\frac{-11+\sqrt{41}}{-8}
$