x^2+18x+10=-9

Solution for x^2+18x+10=-9 equation:

x^2+18x+10=-9

We move all terms to the left:

x^2+18x+10-(-9)=0

We add all the numbers together, and all the variables

x^2+18x+19=0

a = 1; b = 18; c = +19;
Δ = b2-4ac
Δ = 182-4·1·19
Δ = 248
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:

$\sqrt{\Delta}=\sqrt{248}=\sqrt{4*62}=\sqrt{4}*\sqrt{62}=2\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{62}}{2*1}=\frac{-18-2\sqrt{62}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{62}}{2*1}=\frac{-18+2\sqrt{62}}{2}
$