-5n(n-3)=9-4n

Solution for -5n(n-3)=9-4n equation:

-5n(n-3)=9-4n

We move all terms to the left:

-5n(n-3)-(9-4n)=0

We add all the numbers together, and all the variables

-5n(n-3)-(-4n+9)=0

We multiply parentheses

-5n^2+15n-(-4n+9)=0

We get rid of parentheses

-5n^2+15n+4n-9=0

We add all the numbers together, and all the variables

-5n^2+19n-9=0

a = -5; b = 19; c = -9;
Δ = b2-4ac
Δ = 192-4·(-5)·(-9)
Δ = 181
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{-(19)-\sqrt{181}}{2*-5}=\frac{-19-\sqrt{181}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{181}}{2*-5}=\frac{-19+\sqrt{181}}{-10}
$