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x^2/1000-8x+5000=0
We multiply all the terms by the denominator
x^2-8x*1000+5000*1000=0
We add all the numbers together, and all the variables
x^2-8x*1000+5000000=0
Wy multiply elements
x^2-8000x+5000000=0
a = 1; b = -8000; c = +5000000;
Δ = b2-4ac
Δ = -80002-4·1·5000000
Δ = 44000000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{44000000}=\sqrt{4000000*11}=\sqrt{4000000}*\sqrt{11}=2000\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8000)-2000\sqrt{11}}{2*1}=\frac{8000-2000\sqrt{11}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8000)+2000\sqrt{11}}{2*1}=\frac{8000+2000\sqrt{11}}{2} $
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