4x+32=6x(x-4)

Solution for 4x+32=6x(x-4) equation:

4x+32=6x(x-4)

We move all terms to the left:

4x+32-(6x(x-4))=0


We calculate terms in parentheses: -(6x(x-4)), so:

6x(x-4)

We multiply parentheses

6x^2-24x

Back to the equation:

-(6x^2-24x)


We get rid of parentheses

-6x^2+4x+24x+32=0

We add all the numbers together, and all the variables

-6x^2+28x+32=0

a = -6; b = 28; c = +32;
Δ = b2-4ac
Δ = 282-4·(-6)·32
Δ = 1552
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:

$\sqrt{\Delta}=\sqrt{1552}=\sqrt{16*97}=\sqrt{16}*\sqrt{97}=4\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{97}}{2*-6}=\frac{-28-4\sqrt{97}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{97}}{2*-6}=\frac{-28+4\sqrt{97}}{-12}
$