b+3/2b=540

Solution for b+3/2b=540 equation:

b+3/2b=540

We move all terms to the left:

b+3/2b-(540)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We multiply all the terms by the denominator


b*2b-540*2b+3=0

Wy multiply elements

2b^2-1080b+3=0

a = 2; b = -1080; c = +3;
Δ = b2-4ac
Δ = -10802-4·2·3
Δ = 1166376
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:

$\sqrt{\Delta}=\sqrt{1166376}=\sqrt{4*291594}=\sqrt{4}*\sqrt{291594}=2\sqrt{291594}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1080)-2\sqrt{291594}}{2*2}=\frac{1080-2\sqrt{291594}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1080)+2\sqrt{291594}}{2*2}=\frac{1080+2\sqrt{291594}}{4}
$