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

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

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

We move all terms to the left:

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

32x^2-2x-6=0

a = 32; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·32·(-6)
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{193}}{2*32}=\frac{2-2\sqrt{193}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{193}}{2*32}=\frac{2+2\sqrt{193}}{64}
$