4x^2=16x^2+9-24x

Solution for 4x^2=16x^2+9-24x equation:

4x^2=16x^2+9-24x

We move all terms to the left:

4x^2-(16x^2+9-24x)=0

We get rid of parentheses

4x^2-16x^2+24x-9=0

We add all the numbers together, and all the variables

-12x^2+24x-9=0

a = -12; b = 24; c = -9;
Δ = b2-4ac
Δ = 242-4·(-12)·(-9)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12}{2*-12}=\frac{-36}{-24}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12}{2*-12}=\frac{-12}{-24}
=1/2
$