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39x^2-14600x+730000=0
a = 39; b = -14600; c = +730000;
Δ = b2-4ac
Δ = -146002-4·39·730000
Δ = 99280000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{99280000}=\sqrt{40000*2482}=\sqrt{40000}*\sqrt{2482}=200\sqrt{2482}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14600)-200\sqrt{2482}}{2*39}=\frac{14600-200\sqrt{2482}}{78} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14600)+200\sqrt{2482}}{2*39}=\frac{14600+200\sqrt{2482}}{78} $
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