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

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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} $

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