(12(x^2))-288x+1152=0

Solution for (12(x^2))-288x+1152=0 equation:

(12(x^2))-288x+1152=0

determiningTheFunctionDomain
12x^2-288x+1152=0

a = 12; b = -288; c = +1152;
Δ = b2-4ac
Δ = -2882-4·12·1152
Δ = 27648
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:

$\sqrt{\Delta}=\sqrt{27648}=\sqrt{9216*3}=\sqrt{9216}*\sqrt{3}=96\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-96\sqrt{3}}{2*12}=\frac{288-96\sqrt{3}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+96\sqrt{3}}{2*12}=\frac{288+96\sqrt{3}}{24}
$