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12x^2-108x+162=0
a = 12; b = -108; c = +162;
Δ = b2-4ac
Δ = -1082-4·12·162
Δ = 3888
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3888}=\sqrt{1296*3}=\sqrt{1296}*\sqrt{3}=36\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-36\sqrt{3}}{2*12}=\frac{108-36\sqrt{3}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+36\sqrt{3}}{2*12}=\frac{108+36\sqrt{3}}{24} $
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