139b+45(90-90)+2b-90+3/2b=540

Solution for 139b+45(90-90)+2b-90+3/2b=540 equation:

139b+45(90-90)+2b-90+3/2b=540

We move all terms to the left:

139b+45(90-90)+2b-90+3/2b-(540)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


determiningTheFunctionDomain
139b+2b+3/2b-90-540+45(90-90)=0

We add all the numbers together, and all the variables

139b+2b+3/2b-90-540+450=0

We add all the numbers together, and all the variables

141b+3/2b-180=0

We multiply all the terms by the denominator


141b*2b-180*2b+3=0

Wy multiply elements

282b^2-360b+3=0

a = 282; b = -360; c = +3;
Δ = b2-4ac
Δ = -3602-4·282·3
Δ = 126216
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:

$\sqrt{\Delta}=\sqrt{126216}=\sqrt{36*3506}=\sqrt{36}*\sqrt{3506}=6\sqrt{3506}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-6\sqrt{3506}}{2*282}=\frac{360-6\sqrt{3506}}{564}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+6\sqrt{3506}}{2*282}=\frac{360+6\sqrt{3506}}{564}
$