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100000=-614x^2+52000x+20000
We move all terms to the left:
100000-(-614x^2+52000x+20000)=0
We get rid of parentheses
614x^2-52000x-20000+100000=0
We add all the numbers together, and all the variables
614x^2-52000x+80000=0
a = 614; b = -52000; c = +80000;
Δ = b2-4ac
Δ = -520002-4·614·80000
Δ = 2507520000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2507520000}=\sqrt{640000*3918}=\sqrt{640000}*\sqrt{3918}=800\sqrt{3918}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52000)-800\sqrt{3918}}{2*614}=\frac{52000-800\sqrt{3918}}{1228} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52000)+800\sqrt{3918}}{2*614}=\frac{52000+800\sqrt{3918}}{1228} $
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