3(x2-2)=2(x+3)

Solution for 3(x2-2)=2(x+3) equation:

3(x2-2)=2(x+3)

We move all terms to the left:

3(x2-2)-(2(x+3))=0

We add all the numbers together, and all the variables

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

We multiply parentheses

3x^2-(2(x+3))-6=0


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

2(x+3)

We multiply parentheses

2x+6

Back to the equation:

-(2x+6)


We get rid of parentheses

3x^2-2x-6-6=0

We add all the numbers together, and all the variables

3x^2-2x-12=0

a = 3; b = -2; c = -12;
Δ = b2-4ac
Δ = -22-4·3·(-12)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{37}}{2*3}=\frac{2-2\sqrt{37}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{37}}{2*3}=\frac{2+2\sqrt{37}}{6}
$