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12x^2=204
We move all terms to the left:
12x^2-(204)=0
a = 12; b = 0; c = -204;
Δ = b2-4ac
Δ = 02-4·12·(-204)
Δ = 9792
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9792}=\sqrt{576*17}=\sqrt{576}*\sqrt{17}=24\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{17}}{2*12}=\frac{0-24\sqrt{17}}{24} =-\frac{24\sqrt{17}}{24} =-\sqrt{17} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{17}}{2*12}=\frac{0+24\sqrt{17}}{24} =\frac{24\sqrt{17}}{24} =\sqrt{17} $
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