2n2-9n-3=10

Solution for 2n2-9n-3=10 equation:

2n^2-9n-3=10

We move all terms to the left:

2n^2-9n-3-(10)=0

We add all the numbers together, and all the variables

2n^2-9n-13=0

a = 2; b = -9; c = -13;
Δ = b2-4ac
Δ = -92-4·2·(-13)
Δ = 185
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{-(-9)-\sqrt{185}}{2*2}=\frac{9-\sqrt{185}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{185}}{2*2}=\frac{9+\sqrt{185}}{4}
$