X2+66x+5=0

Solution for X2+66x+5=0 equation:

X2+66X+5=0

We add all the numbers together, and all the variables

X^2+66X+5=0

a = 1; b = 66; c = +5;
Δ = b2-4ac
Δ = 662-4·1·5
Δ = 4336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4336}=\sqrt{16*271}=\sqrt{16}*\sqrt{271}=4\sqrt{271}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-4\sqrt{271}}{2*1}=\frac{-66-4\sqrt{271}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+4\sqrt{271}}{2*1}=\frac{-66+4\sqrt{271}}{2}
$