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12x^2-252x+972=0
a = 12; b = -252; c = +972;
Δ = b2-4ac
Δ = -2522-4·12·972
Δ = 16848
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16848}=\sqrt{1296*13}=\sqrt{1296}*\sqrt{13}=36\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-36\sqrt{13}}{2*12}=\frac{252-36\sqrt{13}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+36\sqrt{13}}{2*12}=\frac{252+36\sqrt{13}}{24} $
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