18/4b+21/2b=5

Solution for 18/4b+21/2b=5 equation:

18/4b+21/2b=5

We move all terms to the left:

18/4b+21/2b-(5)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We calculate fractions


36b/8b^2+84b/8b^2-5=0

We multiply all the terms by the denominator


36b+84b-5*8b^2=0

We add all the numbers together, and all the variables

120b-5*8b^2=0

Wy multiply elements

-40b^2+120b=0

a = -40; b = 120; c = 0;
Δ = b2-4ac
Δ = 1202-4·(-40)·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-120}{2*-40}=\frac{-240}{-80}
=+3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+120}{2*-40}=\frac{0}{-80}
=0
$