0.5(n^2-6n+3)=(3n-16)

Solution for 0.5(n^2-6n+3)=(3n-16) equation:

0.5(n^2-6n+3)=(3n-16)

We move all terms to the left:

0.5(n^2-6n+3)-((3n-16))=0

We multiply parentheses

0.5n^2-3n-((3n-16))+1.5=0


We calculate terms in parentheses: -((3n-16)), so:

(3n-16)

We get rid of parentheses

3n-16

Back to the equation:

-(3n-16)


We get rid of parentheses

0.5n^2-3n-3n+16+1.5=0

We add all the numbers together, and all the variables

0.5n^2-6n+17.5=0

a = 0.5; b = -6; c = +17.5;
Δ = b2-4ac
Δ = -62-4·0.5·17.5
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-1}{2*0.5}=\frac{5}{1}
=5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+1}{2*0.5}=\frac{7}{1}
=7
$