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-6x^2+100x-330=0
a = -6; b = 100; c = -330;
Δ = b2-4ac
Δ = 1002-4·(-6)·(-330)
Δ = 2080
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2080}=\sqrt{16*130}=\sqrt{16}*\sqrt{130}=4\sqrt{130}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{130}}{2*-6}=\frac{-100-4\sqrt{130}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{130}}{2*-6}=\frac{-100+4\sqrt{130}}{-12} $
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