30n^2+44n-89=0

Solution for 30n^2+44n-89=0 equation:

30n^2+44n-89=0

a = 30; b = 44; c = -89;
Δ = b2-4ac
Δ = 442-4·30·(-89)
Δ = 12616
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:

$\sqrt{\Delta}=\sqrt{12616}=\sqrt{4*3154}=\sqrt{4}*\sqrt{3154}=2\sqrt{3154}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-2\sqrt{3154}}{2*30}=\frac{-44-2\sqrt{3154}}{60}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+2\sqrt{3154}}{2*30}=\frac{-44+2\sqrt{3154}}{60}
$