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x^2-1840x+6700=0
a = 1; b = -1840; c = +6700;
Δ = b2-4ac
Δ = -18402-4·1·6700
Δ = 3358800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3358800}=\sqrt{3600*933}=\sqrt{3600}*\sqrt{933}=60\sqrt{933}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1840)-60\sqrt{933}}{2*1}=\frac{1840-60\sqrt{933}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1840)+60\sqrt{933}}{2*1}=\frac{1840+60\sqrt{933}}{2} $
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