X^2+10x+10=-7

Solution for X^2+10x+10=-7 equation:

X^2+10X+10=-7

We move all terms to the left:

X^2+10X+10-(-7)=0

We add all the numbers together, and all the variables

X^2+10X+17=0

a = 1; b = 10; c = +17;
Δ = b2-4ac
Δ = 102-4·1·17
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{2}}{2*1}=\frac{-10-4\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{2}}{2*1}=\frac{-10+4\sqrt{2}}{2}
$