2b+3/2b+90+(6+45)+(2b-90)=540

Solution for 2b+3/2b+90+(6+45)+(2b-90)=540 equation:

2b+3/2b+90+(6+45)+(2b-90)=540

We move all terms to the left:

2b+3/2b+90+(6+45)+(2b-90)-(540)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


determiningTheFunctionDomain
2b+3/2b+(2b-90)+90-540+(6+45)=0

We add all the numbers together, and all the variables

2b+3/2b+(2b-90)+90-540+51=0

We add all the numbers together, and all the variables

2b+3/2b+(2b-90)-399=0

We get rid of parentheses

2b+3/2b+2b-90-399=0

We multiply all the terms by the denominator


2b*2b+2b*2b-90*2b-399*2b+3=0

Wy multiply elements

4b^2+4b^2-180b-798b+3=0

We add all the numbers together, and all the variables

8b^2-978b+3=0

a = 8; b = -978; c = +3;
Δ = b2-4ac
Δ = -9782-4·8·3
Δ = 956388
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:

$\sqrt{\Delta}=\sqrt{956388}=\sqrt{4*239097}=\sqrt{4}*\sqrt{239097}=2\sqrt{239097}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-978)-2\sqrt{239097}}{2*8}=\frac{978-2\sqrt{239097}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-978)+2\sqrt{239097}}{2*8}=\frac{978+2\sqrt{239097}}{16}
$