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4b-45+3/2b=540
We move all terms to the left:
4b-45+3/2b-(540)=0
Domain of the equation: 2b!=0We add all the numbers together, and all the variables
b!=0/2
b!=0
b∈R
4b+3/2b-585=0
We multiply all the terms by the denominator
4b*2b-585*2b+3=0
Wy multiply elements
8b^2-1170b+3=0
a = 8; b = -1170; c = +3;
Δ = b2-4ac
Δ = -11702-4·8·3
Δ = 1368804
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}$$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1368804}=\sqrt{4*342201}=\sqrt{4}*\sqrt{342201}=2\sqrt{342201}$$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1170)-2\sqrt{342201}}{2*8}=\frac{1170-2\sqrt{342201}}{16} $$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1170)+2\sqrt{342201}}{2*8}=\frac{1170+2\sqrt{342201}}{16} $
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