3/2b+b+45b+-88b=540

Solution for 3/2b+b+45b+-88b=540 equation:

3/2b+b+45b+-88b=540

We move all terms to the left:

3/2b+b+45b+-88b-(540)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


determiningTheFunctionDomain
3/2b+b+45b-88b-540+=0

We add all the numbers together, and all the variables

-42b+3/2b=0

We multiply all the terms by the denominator


-42b*2b+3=0

Wy multiply elements

-84b^2+3=0

a = -84; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-84)·3
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{7}}{2*-84}=\frac{0-12\sqrt{7}}{-168}
=-\frac{12\sqrt{7}}{-168}
=-\frac{\sqrt{7}}{-14}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{7}}{2*-84}=\frac{0+12\sqrt{7}}{-168}
=\frac{12\sqrt{7}}{-168}
=\frac{\sqrt{7}}{-14}
$