71=x^2+5x+5

Solution for 71=x^2+5x+5 equation:

71=x^2+5x+5

We move all terms to the left:

71-(x^2+5x+5)=0

We get rid of parentheses

-x^2-5x-5+71=0

We add all the numbers together, and all the variables

-1x^2-5x+66=0

a = -1; b = -5; c = +66;
Δ = b2-4ac
Δ = -52-4·(-1)·66
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-17}{2*-1}=\frac{-12}{-2}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+17}{2*-1}=\frac{22}{-2}
=-11
$