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7x-11/x=15
We move all terms to the left:
7x-11/x-(15)=0
Domain of the equation: x!=0We multiply all the terms by the denominator
x∈R
7x*x-15*x-11=0
We add all the numbers together, and all the variables
-15x+7x*x-11=0
Wy multiply elements
7x^2-15x-11=0
a = 7; b = -15; c = -11;
Δ = b2-4ac
Δ = -152-4·7·(-11)
Δ = 533
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{533}}{2*7}=\frac{15-\sqrt{533}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{533}}{2*7}=\frac{15+\sqrt{533}}{14} $
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