7n^2-28n-27=0

Solution for 7n^2-28n-27=0 equation:

7n^2-28n-27=0

a = 7; b = -28; c = -27;
Δ = b2-4ac
Δ = -282-4·7·(-27)
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{385}}{2*7}=\frac{28-2\sqrt{385}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{385}}{2*7}=\frac{28+2\sqrt{385}}{14}
$