4b+3/2b=405

Solution for 4b+3/2b=405 equation:

4b+3/2b=405

We move all terms to the left:

4b+3/2b-(405)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We multiply all the terms by the denominator


4b*2b-405*2b+3=0

Wy multiply elements

8b^2-810b+3=0

a = 8; b = -810; c = +3;
Δ = b2-4ac
Δ = -8102-4·8·3
Δ = 656004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{656004}=\sqrt{4*164001}=\sqrt{4}*\sqrt{164001}=2\sqrt{164001}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-810)-2\sqrt{164001}}{2*8}=\frac{810-2\sqrt{164001}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-810)+2\sqrt{164001}}{2*8}=\frac{810+2\sqrt{164001}}{16}
$