45b+41/2b=540

Solution for 45b+41/2b=540 equation:

45b+41/2b=540

We move all terms to the left:

45b+41/2b-(540)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We multiply all the terms by the denominator


45b*2b-540*2b+41=0

Wy multiply elements

90b^2-1080b+41=0

a = 90; b = -1080; c = +41;
Δ = b2-4ac
Δ = -10802-4·90·41
Δ = 1151640
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:

$\sqrt{\Delta}=\sqrt{1151640}=\sqrt{36*31990}=\sqrt{36}*\sqrt{31990}=6\sqrt{31990}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1080)-6\sqrt{31990}}{2*90}=\frac{1080-6\sqrt{31990}}{180}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1080)+6\sqrt{31990}}{2*90}=\frac{1080+6\sqrt{31990}}{180}
$