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12x^2+102x-66=0
a = 12; b = 102; c = -66;
Δ = b2-4ac
Δ = 1022-4·12·(-66)
Δ = 13572
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13572}=\sqrt{36*377}=\sqrt{36}*\sqrt{377}=6\sqrt{377}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-6\sqrt{377}}{2*12}=\frac{-102-6\sqrt{377}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+6\sqrt{377}}{2*12}=\frac{-102+6\sqrt{377}}{24} $
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