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10x^2+100x+80=20000
We move all terms to the left:
10x^2+100x+80-(20000)=0
We add all the numbers together, and all the variables
10x^2+100x-19920=0
a = 10; b = 100; c = -19920;
Δ = b2-4ac
Δ = 1002-4·10·(-19920)
Δ = 806800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{806800}=\sqrt{400*2017}=\sqrt{400}*\sqrt{2017}=20\sqrt{2017}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{2017}}{2*10}=\frac{-100-20\sqrt{2017}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{2017}}{2*10}=\frac{-100+20\sqrt{2017}}{20} $
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