47=3x(4x-2)

Solution for 47=3x(4x-2) equation:

47=3x(4x-2)

We move all terms to the left:

47-(3x(4x-2))=0


We calculate terms in parentheses: -(3x(4x-2)), so:

3x(4x-2)

We multiply parentheses

12x^2-6x

Back to the equation:

-(12x^2-6x)


We get rid of parentheses

-12x^2+6x+47=0

a = -12; b = 6; c = +47;
Δ = b2-4ac
Δ = 62-4·(-12)·47
Δ = 2292
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:

$\sqrt{\Delta}=\sqrt{2292}=\sqrt{4*573}=\sqrt{4}*\sqrt{573}=2\sqrt{573}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{573}}{2*-12}=\frac{-6-2\sqrt{573}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{573}}{2*-12}=\frac{-6+2\sqrt{573}}{-24}
$