7w^2+10w=-3

Solution for 7w^2+10w=-3 equation:

7w^2+10w=-3

We move all terms to the left:

7w^2+10w-(-3)=0

We add all the numbers together, and all the variables

7w^2+10w+3=0

a = 7; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·7·3
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4}{2*7}=\frac{-14}{14}
=-1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*7}=\frac{-6}{14}
=-3/7
$