513=3x(4x+4)

Solution for 513=3x(4x+4) equation:

513=3x(4x+4)

We move all terms to the left:

513-(3x(4x+4))=0


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

3x(4x+4)

We multiply parentheses

12x^2+12x

Back to the equation:

-(12x^2+12x)


We get rid of parentheses

-12x^2-12x+513=0

a = -12; b = -12; c = +513;
Δ = b2-4ac
Δ = -122-4·(-12)·513
Δ = 24768
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:

$\sqrt{\Delta}=\sqrt{24768}=\sqrt{576*43}=\sqrt{576}*\sqrt{43}=24\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24\sqrt{43}}{2*-12}=\frac{12-24\sqrt{43}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24\sqrt{43}}{2*-12}=\frac{12+24\sqrt{43}}{-24}
$