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10=-100x^2-1700x-6000
We move all terms to the left:
10-(-100x^2-1700x-6000)=0
We get rid of parentheses
100x^2+1700x+6000+10=0
We add all the numbers together, and all the variables
100x^2+1700x+6010=0
a = 100; b = 1700; c = +6010;
Δ = b2-4ac
Δ = 17002-4·100·6010
Δ = 486000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{486000}=\sqrt{32400*15}=\sqrt{32400}*\sqrt{15}=180\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1700)-180\sqrt{15}}{2*100}=\frac{-1700-180\sqrt{15}}{200} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1700)+180\sqrt{15}}{2*100}=\frac{-1700+180\sqrt{15}}{200} $
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