6n^2+37n=455

Solution for 6n^2+37n=455 equation:

6n^2+37n=455

We move all terms to the left:

6n^2+37n-(455)=0

a = 6; b = 37; c = -455;
Δ = b2-4ac
Δ = 372-4·6·(-455)
Δ = 12289
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{-(37)-\sqrt{12289}}{2*6}=\frac{-37-\sqrt{12289}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{12289}}{2*6}=\frac{-37+\sqrt{12289}}{12}
$