81.26=-7.4n(n-7.5)+4.3

Solution for 81.26=-7.4n(n-7.5)+4.3 equation:

81.26=-7.4n(n-7.5)+4.3

We move all terms to the left:

81.26-(-7.4n(n-7.5)+4.3)=0


We calculate terms in parentheses: -(-7.4n(n-7.5)+4.3), so:

-7.4n(n-7.5)+4.3

We multiply parentheses

-7n^2+52.5n+4.3

Back to the equation:

-(-7n^2+52.5n+4.3)


We get rid of parentheses

7n^2-52.5n-4.3+81.26=0

We add all the numbers together, and all the variables

7n^2-52.5n+76.96=0

a = 7; b = -52.5; c = +76.96;
Δ = b2-4ac
Δ = -52.52-4·7·76.96
Δ = 601.37
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{-(-52.5)-\sqrt{601.37}}{2*7}=\frac{52.5-\sqrt{601.37}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52.5)+\sqrt{601.37}}{2*7}=\frac{52.5+\sqrt{601.37}}{14}
$