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12x^2-322x-1288=0
a = 12; b = -322; c = -1288;
Δ = b2-4ac
Δ = -3222-4·12·(-1288)
Δ = 165508
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{165508}=\sqrt{4*41377}=\sqrt{4}*\sqrt{41377}=2\sqrt{41377}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-322)-2\sqrt{41377}}{2*12}=\frac{322-2\sqrt{41377}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-322)+2\sqrt{41377}}{2*12}=\frac{322+2\sqrt{41377}}{24} $
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