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1500+100x-x^2=0
We add all the numbers together, and all the variables
-1x^2+100x+1500=0
a = -1; b = 100; c = +1500;
Δ = b2-4ac
Δ = 1002-4·(-1)·1500
Δ = 16000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-40\sqrt{10}}{2*-1}=\frac{-100-40\sqrt{10}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+40\sqrt{10}}{2*-1}=\frac{-100+40\sqrt{10}}{-2} $
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