7w^2+77w=-210

Solution for 7w^2+77w=-210 equation:

7w^2+77w=-210

We move all terms to the left:

7w^2+77w-(-210)=0

We add all the numbers together, and all the variables

7w^2+77w+210=0

a = 7; b = 77; c = +210;
Δ = b2-4ac
Δ = 772-4·7·210
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(77)-7}{2*7}=\frac{-84}{14}
=-6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(77)+7}{2*7}=\frac{-70}{14}
=-5
$