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5x^2=2000-10x
We move all terms to the left:
5x^2-(2000-10x)=0
We add all the numbers together, and all the variables
5x^2-(-10x+2000)=0
We get rid of parentheses
5x^2+10x-2000=0
a = 5; b = 10; c = -2000;
Δ = b2-4ac
Δ = 102-4·5·(-2000)
Δ = 40100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{40100}=\sqrt{100*401}=\sqrt{100}*\sqrt{401}=10\sqrt{401}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{401}}{2*5}=\frac{-10-10\sqrt{401}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{401}}{2*5}=\frac{-10+10\sqrt{401}}{10} $
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