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5x^2-1500x+125.000=0
We add all the numbers together, and all the variables
5x^2-1500x+125=0
a = 5; b = -1500; c = +125;
Δ = b2-4ac
Δ = -15002-4·5·125
Δ = 2247500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2247500}=\sqrt{2500*899}=\sqrt{2500}*\sqrt{899}=50\sqrt{899}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1500)-50\sqrt{899}}{2*5}=\frac{1500-50\sqrt{899}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1500)+50\sqrt{899}}{2*5}=\frac{1500+50\sqrt{899}}{10} $
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