4x(52-3x)=0

Solution for 4x(52-3x)=0 equation:

4x(52-3x)=0

We add all the numbers together, and all the variables

4x(-3x+52)=0

We multiply parentheses

-12x^2+208x=0

a = -12; b = 208; c = 0;
Δ = b2-4ac
Δ = 2082-4·(-12)·0
Δ = 43264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{43264}=208$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(208)-208}{2*-12}=\frac{-416}{-24}
=17+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(208)+208}{2*-12}=\frac{0}{-24}
=0
$