30w^2+106w+5=-83

Solution for 30w^2+106w+5=-83 equation:

30w^2+106w+5=-83

We move all terms to the left:

30w^2+106w+5-(-83)=0

We add all the numbers together, and all the variables

30w^2+106w+88=0

a = 30; b = 106; c = +88;
Δ = b2-4ac
Δ = 1062-4·30·88
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(106)-26}{2*30}=\frac{-132}{60}
=-2+1/5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(106)+26}{2*30}=\frac{-80}{60}
=-1+1/3
$