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X(47-X)=550
We move all terms to the left:
X(47-X)-(550)=0
We add all the numbers together, and all the variables
X(-1X+47)-550=0
We multiply parentheses
-1X^2+47X-550=0
a = -1; b = 47; c = -550;
Δ = b2-4ac
Δ = 472-4·(-1)·(-550)
Δ = 9
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{9}=3$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-3}{2*-1}=\frac{-50}{-2} =+25 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+3}{2*-1}=\frac{-44}{-2} =+22 $
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