1/2b+9/4b=3/2b+5

Solution for 1/2b+9/4b=3/2b+5 equation:

1/2b+9/4b=3/2b+5

We move all terms to the left:

1/2b+9/4b-(3/2b+5)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R



Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 2b+5)!=0

b∈R


We get rid of parentheses

1/2b+9/4b-3/2b-5=0

We calculate fractions


(-12b+1)/8b^2+18b/8b^2-5=0

We multiply all the terms by the denominator


(-12b+1)+18b-5*8b^2=0

We add all the numbers together, and all the variables

18b+(-12b+1)-5*8b^2=0

Wy multiply elements

-40b^2+18b+(-12b+1)=0

We get rid of parentheses

-40b^2+18b-12b+1=0

We add all the numbers together, and all the variables

-40b^2+6b+1=0

a = -40; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-40)·1
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*-40}=\frac{-20}{-80}
=1/4
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*-40}=\frac{8}{-80}
=-1/10
$