9(4b^2-1)=2(9b^2+3)

Solution for 9(4b^2-1)=2(9b^2+3) equation:

9(4b^2-1)=2(9b^2+3)

We move all terms to the left:

9(4b^2-1)-(2(9b^2+3))=0

We multiply parentheses

36b^2-(2(9b^2+3))-9=0


We calculate terms in parentheses: -(2(9b^2+3)), so:

2(9b^2+3)

We multiply parentheses

18b^2+6

Back to the equation:

-(18b^2+6)


We get rid of parentheses

36b^2-18b^2-6-9=0

We add all the numbers together, and all the variables

18b^2-15=0

a = 18; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·18·(-15)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{30}}{2*18}=\frac{0-6\sqrt{30}}{36}
=-\frac{6\sqrt{30}}{36}
=-\frac{\sqrt{30}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{30}}{2*18}=\frac{0+6\sqrt{30}}{36}
=\frac{6\sqrt{30}}{36}
=\frac{\sqrt{30}}{6}
$