4(3x^2-110x+600)=0

Solution for 4(3x^2-110x+600)=0 equation:

4(3x^2-110x+600)=0

We multiply parentheses

12x^2-440x+2400=0

a = 12; b = -440; c = +2400;
Δ = b2-4ac
Δ = -4402-4·12·2400
Δ = 78400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{78400}=280$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-440)-280}{2*12}=\frac{160}{24}
=6+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-440)+280}{2*12}=\frac{720}{24}
=30
$