4=6x(x-2)

Solution for 4=6x(x-2) equation:

4=6x(x-2)

We move all terms to the left:

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


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

6x(x-2)

We multiply parentheses

6x^2-12x

Back to the equation:

-(6x^2-12x)


We get rid of parentheses

-6x^2+12x+4=0

a = -6; b = 12; c = +4;
Δ = b2-4ac
Δ = 122-4·(-6)·4
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{15}}{2*-6}=\frac{-12-4\sqrt{15}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{15}}{2*-6}=\frac{-12+4\sqrt{15}}{-12}
$