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6x^2-200x+1200=0
a = 6; b = -200; c = +1200;
Δ = b2-4ac
Δ = -2002-4·6·1200
Δ = 11200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-40\sqrt{7}}{2*6}=\frac{200-40\sqrt{7}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+40\sqrt{7}}{2*6}=\frac{200+40\sqrt{7}}{12} $
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