2n(n=22)+9=

Solution for 2n(n=22)+9= equation:

2n(n=22)+9=

We move all terms to the left:

2n(n-(22)+9)=0

We add all the numbers together, and all the variables

2n(n-13)=0

We multiply parentheses

2n^2-26n=0

a = 2; b = -26; c = 0;
Δ = b2-4ac
Δ = -262-4·2·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-26}{2*2}=\frac{0}{4}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+26}{2*2}=\frac{52}{4}
=13
$