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3x=50/x-19
We move all terms to the left:
3x-(50/x-19)=0
Domain of the equation: x-19)!=0We get rid of parentheses
x∈R
3x-50/x+19=0
We multiply all the terms by the denominator
3x*x+19*x-50=0
We add all the numbers together, and all the variables
19x+3x*x-50=0
Wy multiply elements
3x^2+19x-50=0
a = 3; b = 19; c = -50;
Δ = b2-4ac
Δ = 192-4·3·(-50)
Δ = 961
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{961}=31$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-31}{2*3}=\frac{-50}{6} =-8+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+31}{2*3}=\frac{12}{6} =2 $
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