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80x+800-x^2-20x=0
We add all the numbers together, and all the variables
-1x^2+60x+800=0
a = -1; b = 60; c = +800;
Δ = b2-4ac
Δ = 602-4·(-1)·800
Δ = 6800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6800}=\sqrt{400*17}=\sqrt{400}*\sqrt{17}=20\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-20\sqrt{17}}{2*-1}=\frac{-60-20\sqrt{17}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+20\sqrt{17}}{2*-1}=\frac{-60+20\sqrt{17}}{-2} $
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