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30000+600x-3000+600x=2500-x^2
We move all terms to the left:
30000+600x-3000+600x-(2500-x^2)=0
We add all the numbers together, and all the variables
-(2500-x^2)+1200x+27000=0
We get rid of parentheses
x^2+1200x-2500+27000=0
We add all the numbers together, and all the variables
x^2+1200x+24500=0
a = 1; b = 1200; c = +24500;
Δ = b2-4ac
Δ = 12002-4·1·24500
Δ = 1342000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1342000}=\sqrt{400*3355}=\sqrt{400}*\sqrt{3355}=20\sqrt{3355}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1200)-20\sqrt{3355}}{2*1}=\frac{-1200-20\sqrt{3355}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1200)+20\sqrt{3355}}{2*1}=\frac{-1200+20\sqrt{3355}}{2} $
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