183b-450+3/2b=540

Solution for 183b-450+3/2b=540 equation:

183b-450+3/2b=540

We move all terms to the left:

183b-450+3/2b-(540)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

183b+3/2b-990=0

We multiply all the terms by the denominator


183b*2b-990*2b+3=0

Wy multiply elements

366b^2-1980b+3=0

a = 366; b = -1980; c = +3;
Δ = b2-4ac
Δ = -19802-4·366·3
Δ = 3916008
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:

$\sqrt{\Delta}=\sqrt{3916008}=\sqrt{36*108778}=\sqrt{36}*\sqrt{108778}=6\sqrt{108778}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1980)-6\sqrt{108778}}{2*366}=\frac{1980-6\sqrt{108778}}{732}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1980)+6\sqrt{108778}}{2*366}=\frac{1980+6\sqrt{108778}}{732}
$