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460x^2+40x-1000=0
a = 460; b = 40; c = -1000;
Δ = b2-4ac
Δ = 402-4·460·(-1000)
Δ = 1841600
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1841600}=\sqrt{1600*1151}=\sqrt{1600}*\sqrt{1151}=40\sqrt{1151}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40\sqrt{1151}}{2*460}=\frac{-40-40\sqrt{1151}}{920} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40\sqrt{1151}}{2*460}=\frac{-40+40\sqrt{1151}}{920} $
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