B+3/2b+(2b-90)+90=540

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

+3/2B+(2B-90)+90=540

We move all terms to the left:

+3/2B+(2B-90)+90-(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

3/2B+(2B-90)-450=0

We get rid of parentheses

3/2B+2B-90-450=0

We multiply all the terms by the denominator


2B*2B-90*2B-450*2B+3=0

Wy multiply elements

4B^2-180B-900B+3=0

We add all the numbers together, and all the variables

4B^2-1080B+3=0

a = 4; b = -1080; c = +3;
Δ = b2-4ac
Δ = -10802-4·4·3
Δ = 1166352
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:

$\sqrt{\Delta}=\sqrt{1166352}=\sqrt{35344*33}=\sqrt{35344}*\sqrt{33}=188\sqrt{33}$
$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1080)-188\sqrt{33}}{2*4}=\frac{1080-188\sqrt{33}}{8}
$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1080)+188\sqrt{33}}{2*4}=\frac{1080+188\sqrt{33}}{8}
$