4x2+x2+x(x+6)=432

Solution for 4x2+x2+x(x+6)=432 equation:

4x^2+x2+x(x+6)=432

We move all terms to the left:

4x^2+x2+x(x+6)-(432)=0

We add all the numbers together, and all the variables

5x^2+x(x+6)-432=0

We multiply parentheses

5x^2+x^2+6x-432=0

We add all the numbers together, and all the variables

6x^2+6x-432=0

a = 6; b = 6; c = -432;
Δ = b2-4ac
Δ = 62-4·6·(-432)
Δ = 10404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10404}=102$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-102}{2*6}=\frac{-108}{12}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+102}{2*6}=\frac{96}{12}
=8
$