6n2-3n-92=n2

Solution for 6n2-3n-92=n2 equation:

6n^2-3n-92=n2

We move all terms to the left:

6n^2-3n-92-(n2)=0

We add all the numbers together, and all the variables

5n^2-3n-92=0

a = 5; b = -3; c = -92;
Δ = b2-4ac
Δ = -32-4·5·(-92)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-43}{2*5}=\frac{-40}{10}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+43}{2*5}=\frac{46}{10}
=4+3/5
$