-7a^2-65a-1=0

Solution for -7a^2-65a-1=0 equation:

-7a^2-65a-1=0

a = -7; b = -65; c = -1;
Δ = b2-4ac
Δ = -652-4·(-7)·(-1)
Δ = 4197
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-\sqrt{4197}}{2*-7}=\frac{65-\sqrt{4197}}{-14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{4197}}{2*-7}=\frac{65+\sqrt{4197}}{-14}
$