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(-x)(x-100)=100
We move all terms to the left:
(-x)(x-100)-(100)=0
We add all the numbers together, and all the variables
(-1x)(x-100)-100=0
We multiply parentheses ..
(-1x^2+100x)-100=0
We get rid of parentheses
-1x^2+100x-100=0
a = -1; b = 100; c = -100;
Δ = b2-4ac
Δ = 1002-4·(-1)·(-100)
Δ = 9600
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-40\sqrt{6}}{2*-1}=\frac{-100-40\sqrt{6}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+40\sqrt{6}}{2*-1}=\frac{-100+40\sqrt{6}}{-2} $
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