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30x^2-1880x+2400=0
a = 30; b = -1880; c = +2400;
Δ = b2-4ac
Δ = -18802-4·30·2400
Δ = 3246400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3246400}=\sqrt{1600*2029}=\sqrt{1600}*\sqrt{2029}=40\sqrt{2029}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1880)-40\sqrt{2029}}{2*30}=\frac{1880-40\sqrt{2029}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1880)+40\sqrt{2029}}{2*30}=\frac{1880+40\sqrt{2029}}{60} $
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