w2+7w=-10

Solution for w2+7w=-10 equation:

w2+7w=-10

We move all terms to the left:

w2+7w-(-10)=0

We add all the numbers together, and all the variables

w^2+7w+10=0

a = 1; b = 7; c = +10;
Δ = b2-4ac
Δ = 72-4·1·10
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3}{2*1}=\frac{-10}{2}
=-5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*1}=\frac{-4}{2}
=-2
$