4(3x^2-60x+200)=0

Solution for 4(3x^2-60x+200)=0 equation:

4(3x^2-60x+200)=0

We multiply parentheses

12x^2-240x+800=0

a = 12; b = -240; c = +800;
Δ = b2-4ac
Δ = -2402-4·12·800
Δ = 19200
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:

$\sqrt{\Delta}=\sqrt{19200}=\sqrt{6400*3}=\sqrt{6400}*\sqrt{3}=80\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-80\sqrt{3}}{2*12}=\frac{240-80\sqrt{3}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+80\sqrt{3}}{2*12}=\frac{240+80\sqrt{3}}{24}
$