2n^2+2n-74=0

Solution for 2n^2+2n-74=0 equation:

2n^2+2n-74=0

a = 2; b = 2; c = -74;
Δ = b2-4ac
Δ = 22-4·2·(-74)
Δ = 596
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:

$\sqrt{\Delta}=\sqrt{596}=\sqrt{4*149}=\sqrt{4}*\sqrt{149}=2\sqrt{149}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{149}}{2*2}=\frac{-2-2\sqrt{149}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{149}}{2*2}=\frac{-2+2\sqrt{149}}{4}
$