4b^2+5b=21

Solution for 4b^2+5b=21 equation:

4b^2+5b=21

We move all terms to the left:

4b^2+5b-(21)=0

a = 4; b = 5; c = -21;
Δ = b2-4ac
Δ = 52-4·4·(-21)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*4}=\frac{-24}{8}
=-3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*4}=\frac{14}{8}
=1+3/4
$