4b^2=84-16b

Solution for 4b^2=84-16b equation:

4b^2=84-16b

We move all terms to the left:

4b^2-(84-16b)=0

We add all the numbers together, and all the variables

4b^2-(-16b+84)=0

We get rid of parentheses

4b^2+16b-84=0

a = 4; b = 16; c = -84;
Δ = b2-4ac
Δ = 162-4·4·(-84)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-40}{2*4}=\frac{-56}{8}
=-7
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+40}{2*4}=\frac{24}{8}
=3
$