96(x-1)(2x-1)=0

Solution for 96(x-1)(2x-1)=0 equation:

96(x-1)(2x-1)=0

We multiply parentheses ..

96(+2x^2-1x-2x+1)=0

We multiply parentheses

192x^2-96x-192x+96=0

We add all the numbers together, and all the variables

192x^2-288x+96=0

a = 192; b = -288; c = +96;
Δ = b2-4ac
Δ = -2882-4·192·96
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-96}{2*192}=\frac{192}{384}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+96}{2*192}=\frac{384}{384}
=1
$