4b^2-84=-5b

Solution for 4b^2-84=-5b equation:

4b^2-84=-5b

We move all terms to the left:

4b^2-84-(-5b)=0

We get rid of parentheses

4b^2+5b-84=0

a = 4; b = 5; c = -84;
Δ = b2-4ac
Δ = 52-4·4·(-84)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-37}{2*4}=\frac{-42}{8}
=-5+1/4
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+37}{2*4}=\frac{32}{8}
=4
$