0.9b(0.5b+0.8)-0.4(0.6b+1.8)=0.21b

Solution for 0.9b(0.5b+0.8)-0.4(0.6b+1.8)=0.21b equation:

0.9b(0.5b+0.8)-0.4(0.6b+1.8)=0.21b

We move all terms to the left:

0.9b(0.5b+0.8)-0.4(0.6b+1.8)-(0.21b)=0

We add all the numbers together, and all the variables

0.9b(0.5b+0.8)-0.4(0.6b+1.8)-(+0.21b)=0

We multiply parentheses

0b^2+0b-0b-(+0.21b)-0.72=0

We get rid of parentheses

0b^2+0b-0b-0.21b-0.72=0

We add all the numbers together, and all the variables

b^2-0.21b-0.72=0

a = 1; b = -0.21; c = -0.72;
Δ = b2-4ac
Δ = -0.212-4·1·(-0.72)
Δ = 2.9241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.21)-\sqrt{2.9241}}{2*1}=\frac{0.21-\sqrt{2.9241}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.21)+\sqrt{2.9241}}{2*1}=\frac{0.21+\sqrt{2.9241}}{2}
$