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x(1+x)=20000000
We move all terms to the left:
x(1+x)-(20000000)=0
We add all the numbers together, and all the variables
x(x+1)-20000000=0
We multiply parentheses
x^2+x-20000000=0
a = 1; b = 1; c = -20000000;
Δ = b2-4ac
Δ = 12-4·1·(-20000000)
Δ = 80000001
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{80000001}=\sqrt{9*8888889}=\sqrt{9}*\sqrt{8888889}=3\sqrt{8888889}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{8888889}}{2*1}=\frac{-1-3\sqrt{8888889}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{8888889}}{2*1}=\frac{-1+3\sqrt{8888889}}{2} $
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