3/2b+6+1/2b=15*2b

Solution for 3/2b+6+1/2b=15*2b equation:

3/2b+6+1/2b=15*2b

We move all terms to the left:

3/2b+6+1/2b-(15*2b)=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+1/2b-(+15*2b)+6=0

We get rid of parentheses

3/2b+1/2b-15*2b+6=0

We multiply all the terms by the denominator


-(15*2b)*2b+6*2b+3+1=0

We add all the numbers together, and all the variables

-(+15*2b)*2b+6*2b+3+1=0

We add all the numbers together, and all the variables

-(+15*2b)*2b+6*2b+4=0

We multiply parentheses

-60b^2+6*2b+4=0

Wy multiply elements

-60b^2+12b+4=0

a = -60; b = 12; c = +4;
Δ = b2-4ac
Δ = 122-4·(-60)·4
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{69}}{2*-60}=\frac{-12-4\sqrt{69}}{-120}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{69}}{2*-60}=\frac{-12+4\sqrt{69}}{-120}
$