x^2+10x+9=-2x-4

Solution for x^2+10x+9=-2x-4 equation:

x^2+10x+9=-2x-4

We move all terms to the left:

x^2+10x+9-(-2x-4)=0

We get rid of parentheses

x^2+10x+2x+4+9=0

We add all the numbers together, and all the variables

x^2+12x+13=0

a = 1; b = 12; c = +13;
Δ = b2-4ac
Δ = 122-4·1·13
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{23}}{2*1}=\frac{-12-2\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{23}}{2*1}=\frac{-12+2\sqrt{23}}{2}
$