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1x^2-460x+24.000=0
We add all the numbers together, and all the variables
x^2-460x+24=0
a = 1; b = -460; c = +24;
Δ = b2-4ac
Δ = -4602-4·1·24
Δ = 211504
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{211504}=\sqrt{16*13219}=\sqrt{16}*\sqrt{13219}=4\sqrt{13219}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-460)-4\sqrt{13219}}{2*1}=\frac{460-4\sqrt{13219}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-460)+4\sqrt{13219}}{2*1}=\frac{460+4\sqrt{13219}}{2} $
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