7n^2+52n-53=0

Solution for 7n^2+52n-53=0 equation:

7n^2+52n-53=0

a = 7; b = 52; c = -53;
Δ = b2-4ac
Δ = 522-4·7·(-53)
Δ = 4188
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:

$\sqrt{\Delta}=\sqrt{4188}=\sqrt{4*1047}=\sqrt{4}*\sqrt{1047}=2\sqrt{1047}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-2\sqrt{1047}}{2*7}=\frac{-52-2\sqrt{1047}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+2\sqrt{1047}}{2*7}=\frac{-52+2\sqrt{1047}}{14}
$