x2+18x+71=0

Solution for x2+18x+71=0 equation:

x2+18x+71=0

We add all the numbers together, and all the variables

x^2+18x+71=0

a = 1; b = 18; c = +71;
Δ = b2-4ac
Δ = 182-4·1·71
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{10}}{2*1}=\frac{-18-2\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{10}}{2*1}=\frac{-18+2\sqrt{10}}{2}
$