(3/2)b=6*1/4

Solution for (3/2)b=6*1/4 equation:

(3/2)b=6*1/4

We move all terms to the left:

(3/2)b-(6*1/4)=0


Domain of the equation: 2)b!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

(+3/2)b-(+6*1/4)=0

We multiply parentheses

3b^2-(+6*1/4)=0

We get rid of parentheses

3b^2-6*1/4=0

We multiply all the terms by the denominator


3b^2*4-6*1=0

We add all the numbers together, and all the variables

3b^2*4-6=0

Wy multiply elements

12b^2-6=0

a = 12; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·12·(-6)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*12}=\frac{0-12\sqrt{2}}{24}
=-\frac{12\sqrt{2}}{24}
=-\frac{\sqrt{2}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*12}=\frac{0+12\sqrt{2}}{24}
=\frac{12\sqrt{2}}{24}
=\frac{\sqrt{2}}{2}
$