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19/44x=x-850
We move all terms to the left:
19/44x-(x-850)=0
Domain of the equation: 44x!=0We get rid of parentheses
x!=0/44
x!=0
x∈R
19/44x-x+850=0
We multiply all the terms by the denominator
-x*44x+850*44x+19=0
Wy multiply elements
-44x^2+37400x+19=0
a = -44; b = 37400; c = +19;
Δ = b2-4ac
Δ = 374002-4·(-44)·19
Δ = 1398763344
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1398763344}=\sqrt{16*87422709}=\sqrt{16}*\sqrt{87422709}=4\sqrt{87422709}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37400)-4\sqrt{87422709}}{2*-44}=\frac{-37400-4\sqrt{87422709}}{-88} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37400)+4\sqrt{87422709}}{2*-44}=\frac{-37400+4\sqrt{87422709}}{-88} $
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