-8w-3=4w^2

Solution for -8w-3=4w^2 equation:

-8w-3=4w^2

We move all terms to the left:

-8w-3-(4w^2)=0

determiningTheFunctionDomain
-4w^2-8w-3=0

a = -4; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·(-4)·(-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{-(-8)-4}{2*-4}=\frac{4}{-8}
=-1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4}{2*-4}=\frac{12}{-8}
=-1+1/2
$