16x(1-2x)=4(x-3)

Solution for 16x(1-2x)=4(x-3) equation:

16x(1-2x)=4(x-3)

We move all terms to the left:

16x(1-2x)-(4(x-3))=0

We add all the numbers together, and all the variables

16x(-2x+1)-(4(x-3))=0

We multiply parentheses

-32x^2+16x-(4(x-3))=0


We calculate terms in parentheses: -(4(x-3)), so:

4(x-3)

We multiply parentheses

4x-12

Back to the equation:

-(4x-12)


We get rid of parentheses

-32x^2+16x-4x+12=0

We add all the numbers together, and all the variables

-32x^2+12x+12=0

a = -32; b = 12; c = +12;
Δ = b2-4ac
Δ = 122-4·(-32)·12
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{105}}{2*-32}=\frac{-12-4\sqrt{105}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{105}}{2*-32}=\frac{-12+4\sqrt{105}}{-64}
$