31w-5w^2=-28

Solution for 31w-5w^2=-28 equation:

31w-5w^2=-28

We move all terms to the left:

31w-5w^2-(-28)=0

We add all the numbers together, and all the variables

-5w^2+31w+28=0

a = -5; b = 31; c = +28;
Δ = b2-4ac
Δ = 312-4·(-5)·28
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-39}{2*-5}=\frac{-70}{-10}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+39}{2*-5}=\frac{8}{-10}
=-4/5
$