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x+4/x-7=4
We move all terms to the left:
x+4/x-7-(4)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
x+4/x-11=0
We multiply all the terms by the denominator
x*x-11*x+4=0
We add all the numbers together, and all the variables
-11x+x*x+4=0
Wy multiply elements
x^2-11x+4=0
a = 1; b = -11; c = +4;
Δ = b2-4ac
Δ = -112-4·1·4
Δ = 105
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{-(-11)-\sqrt{105}}{2*1}=\frac{11-\sqrt{105}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{105}}{2*1}=\frac{11+\sqrt{105}}{2} $
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