3n2+237n-4590=0

Solution for 3n2+237n-4590=0 equation:

3n^2+237n-4590=0

a = 3; b = 237; c = -4590;
Δ = b2-4ac
Δ = 2372-4·3·(-4590)
Δ = 111249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{111249}=\sqrt{9*12361}=\sqrt{9}*\sqrt{12361}=3\sqrt{12361}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(237)-3\sqrt{12361}}{2*3}=\frac{-237-3\sqrt{12361}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(237)+3\sqrt{12361}}{2*3}=\frac{-237+3\sqrt{12361}}{6}
$