9x^2=2(3x+1)

Solution for 9x^2=2(3x+1) equation:

9x^2=2(3x+1)

We move all terms to the left:

9x^2-(2(3x+1))=0


We calculate terms in parentheses: -(2(3x+1)), so:

2(3x+1)

We multiply parentheses

6x+2

Back to the equation:

-(6x+2)


We get rid of parentheses

9x^2-6x-2=0

a = 9; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·9·(-2)
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{3}}{2*9}=\frac{6-6\sqrt{3}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{3}}{2*9}=\frac{6+6\sqrt{3}}{18}
$