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x+6/x-3=10
We move all terms to the left:
x+6/x-3-(10)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
x+6/x-13=0
We multiply all the terms by the denominator
x*x-13*x+6=0
We add all the numbers together, and all the variables
-13x+x*x+6=0
Wy multiply elements
x^2-13x+6=0
a = 1; b = -13; c = +6;
Δ = b2-4ac
Δ = -132-4·1·6
Δ = 145
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{-(-13)-\sqrt{145}}{2*1}=\frac{13-\sqrt{145}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{145}}{2*1}=\frac{13+\sqrt{145}}{2} $
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