2b+3/2b+150=360

Solution for 2b+3/2b+150=360 equation:

2b+3/2b+150=360

We move all terms to the left:

2b+3/2b+150-(360)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

2b+3/2b-210=0

We multiply all the terms by the denominator


2b*2b-210*2b+3=0

Wy multiply elements

4b^2-420b+3=0

a = 4; b = -420; c = +3;
Δ = b2-4ac
Δ = -4202-4·4·3
Δ = 176352
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:

$\sqrt{\Delta}=\sqrt{176352}=\sqrt{16*11022}=\sqrt{16}*\sqrt{11022}=4\sqrt{11022}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-4\sqrt{11022}}{2*4}=\frac{420-4\sqrt{11022}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+4\sqrt{11022}}{2*4}=\frac{420+4\sqrt{11022}}{8}
$