45b+4b+1/2b=540

Solution for 45b+4b+1/2b=540 equation:

45b+4b+1/2b=540

We move all terms to the left:

45b+4b+1/2b-(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

49b+1/2b-540=0

We multiply all the terms by the denominator


49b*2b-540*2b+1=0

Wy multiply elements

98b^2-1080b+1=0

a = 98; b = -1080; c = +1;
Δ = b2-4ac
Δ = -10802-4·98·1
Δ = 1166008
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:

$\sqrt{\Delta}=\sqrt{1166008}=\sqrt{4*291502}=\sqrt{4}*\sqrt{291502}=2\sqrt{291502}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1080)-2\sqrt{291502}}{2*98}=\frac{1080-2\sqrt{291502}}{196}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1080)+2\sqrt{291502}}{2*98}=\frac{1080+2\sqrt{291502}}{196}
$