5n*n-3n-296=0

Solution for 5n*n-3n-296=0 equation:

5n*n-3n-296=0

We add all the numbers together, and all the variables

-3n+5n*n-296=0

Wy multiply elements

5n^2-3n-296=0

a = 5; b = -3; c = -296;
Δ = b2-4ac
Δ = -32-4·5·(-296)
Δ = 5929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5929}=77$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-77}{2*5}=\frac{-74}{10}
=-7+2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+77}{2*5}=\frac{80}{10}
=8
$