3/2b+46b=360

Solution for 3/2b+46b=360 equation:

3/2b+46b=360

We move all terms to the left:

3/2b+46b-(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

46b+3/2b-360=0

We multiply all the terms by the denominator


46b*2b-360*2b+3=0

Wy multiply elements

92b^2-720b+3=0

a = 92; b = -720; c = +3;
Δ = b2-4ac
Δ = -7202-4·92·3
Δ = 517296
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:

$\sqrt{\Delta}=\sqrt{517296}=\sqrt{16*32331}=\sqrt{16}*\sqrt{32331}=4\sqrt{32331}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-4\sqrt{32331}}{2*92}=\frac{720-4\sqrt{32331}}{184}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+4\sqrt{32331}}{2*92}=\frac{720+4\sqrt{32331}}{184}
$