2n^2-11n=-9

Solution for 2n^2-11n=-9 equation:

2n^2-11n=-9

We move all terms to the left:

2n^2-11n-(-9)=0

We add all the numbers together, and all the variables

2n^2-11n+9=0

a = 2; b = -11; c = +9;
Δ = b2-4ac
Δ = -112-4·2·9
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-7}{2*2}=\frac{4}{4}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+7}{2*2}=\frac{18}{4}
=4+1/2
$