4x(x+6)-x2=5x2

Solution for 4x(x+6)-x2=5x2 equation:

4x(x+6)-x2=5x^2

We move all terms to the left:

4x(x+6)-x2-(5x^2)=0

determiningTheFunctionDomain
-5x^2+4x(x+6)-x2=0

We add all the numbers together, and all the variables

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

We multiply parentheses

-6x^2+4x^2+24x=0

We add all the numbers together, and all the variables

-2x^2+24x=0

a = -2; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-2)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-2}=\frac{-48}{-4}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-2}=\frac{0}{-4}
=0
$