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x+6/x-4=11
We move all terms to the left:
x+6/x-4-(11)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
x+6/x-15=0
We multiply all the terms by the denominator
x*x-15*x+6=0
We add all the numbers together, and all the variables
-15x+x*x+6=0
Wy multiply elements
x^2-15x+6=0
a = 1; b = -15; c = +6;
Δ = b2-4ac
Δ = -152-4·1·6
Δ = 201
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{201}}{2*1}=\frac{15-\sqrt{201}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{201}}{2*1}=\frac{15+\sqrt{201}}{2} $
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