-3n(n-5)=8-2n

Solution for -3n(n-5)=8-2n equation:

-3n(n-5)=8-2n

We move all terms to the left:

-3n(n-5)-(8-2n)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

-3n^2+15n-(-2n+8)=0

We get rid of parentheses

-3n^2+15n+2n-8=0

We add all the numbers together, and all the variables

-3n^2+17n-8=0

a = -3; b = 17; c = -8;
Δ = b2-4ac
Δ = 172-4·(-3)·(-8)
Δ = 193
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{-(17)-\sqrt{193}}{2*-3}=\frac{-17-\sqrt{193}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{193}}{2*-3}=\frac{-17+\sqrt{193}}{-6}
$