2(54-21b+2b^2)=0

Solution for 2(54-21b+2b^2)=0 equation:

2(54-21b+2b^2)=0

We multiply parentheses

4b^2-42b+108=0

a = 4; b = -42; c = +108;
Δ = b2-4ac
Δ = -422-4·4·108
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6}{2*4}=\frac{36}{8}
=4+1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6}{2*4}=\frac{48}{8}
=6
$