2n2-3n-4=6

Solution for 2n2-3n-4=6 equation:

2n^2-3n-4=6

We move all terms to the left:

2n^2-3n-4-(6)=0

We add all the numbers together, and all the variables

2n^2-3n-10=0

a = 2; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·2·(-10)
Δ = 89
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{-(-3)-\sqrt{89}}{2*2}=\frac{3-\sqrt{89}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{89}}{2*2}=\frac{3+\sqrt{89}}{4}
$