3/4b+5/2b=4

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

3/4b+5/2b=4

We move all terms to the left:

3/4b+5/2b-(4)=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


6b/8b^2+20b/8b^2-4=0

We multiply all the terms by the denominator


6b+20b-4*8b^2=0

We add all the numbers together, and all the variables

26b-4*8b^2=0

Wy multiply elements

-32b^2+26b=0

a = -32; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·(-32)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*-32}=\frac{-52}{-64}
=13/16
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*-32}=\frac{0}{-64}
=0
$