4n^2+2n-72=0

Solution for 4n^2+2n-72=0 equation:

4n^2+2n-72=0

a = 4; b = 2; c = -72;
Δ = b2-4ac
Δ = 22-4·4·(-72)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-34}{2*4}=\frac{-36}{8}
=-4+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+34}{2*4}=\frac{32}{8}
=4
$