10.26n=4n(n-2.1)

Solution for 10.26n=4n(n-2.1) equation:

10.26n=4n(n-2.1)

We move all terms to the left:

10.26n-(4n(n-2.1))=0


We calculate terms in parentheses: -(4n(n-2.1)), so:

4n(n-2.1)

We multiply parentheses

4n^2-8.4n

Back to the equation:

-(4n^2-8.4n)


We get rid of parentheses

-4n^2+10.26n+8.4n=0

We add all the numbers together, and all the variables

-4n^2+18.66n=0

a = -4; b = 18.66; c = 0;
Δ = b2-4ac
Δ = 18.662-4·(-4)·0
Δ = 348.1956
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{-(18.66)-\sqrt{348.1956}}{2*-4}=\frac{-18.66-\sqrt{348.1956}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18.66)+\sqrt{348.1956}}{2*-4}=\frac{-18.66+\sqrt{348.1956}}{-8}
$