432=x(x/2+6)

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

432=x(x/2+6)

We move all terms to the left:

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

We multiply all the terms by the denominator


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


We calculate terms in parentheses: -(x(x+432*2+6)), so:

x(x+432*2+6)

We add all the numbers together, and all the variables

x(x+870)

We multiply parentheses

x^2+870x

Back to the equation:

-(x^2+870x)


We get rid of parentheses

-x^2-870x=0

We add all the numbers together, and all the variables

-1x^2-870x=0

a = -1; b = -870; c = 0;
Δ = b2-4ac
Δ = -8702-4·(-1)·0
Δ = 756900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{756900}=870$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-870)-870}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-870)+870}{2*-1}=\frac{1740}{-2}
=-870
$