432=x(2x+6)

Solution for 432=x(2x+6) equation:

432=x(2x+6)

We move all terms to the left:

432-(x(2x+6))=0


We calculate terms in parentheses: -(x(2x+6)), so:

x(2x+6)

We multiply parentheses

2x^2+6x

Back to the equation:

-(2x^2+6x)


We get rid of parentheses

-2x^2-6x+432=0

a = -2; b = -6; c = +432;
Δ = b2-4ac
Δ = -62-4·(-2)·432
Δ = 3492
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:

$\sqrt{\Delta}=\sqrt{3492}=\sqrt{36*97}=\sqrt{36}*\sqrt{97}=6\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{97}}{2*-2}=\frac{6-6\sqrt{97}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{97}}{2*-2}=\frac{6+6\sqrt{97}}{-4}
$