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12x^2-282x+1153=0
a = 12; b = -282; c = +1153;
Δ = b2-4ac
Δ = -2822-4·12·1153
Δ = 24180
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24180}=\sqrt{4*6045}=\sqrt{4}*\sqrt{6045}=2\sqrt{6045}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-282)-2\sqrt{6045}}{2*12}=\frac{282-2\sqrt{6045}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-282)+2\sqrt{6045}}{2*12}=\frac{282+2\sqrt{6045}}{24} $
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