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8x+9/x-11=10
We move all terms to the left:
8x+9/x-11-(10)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
8x+9/x-21=0
We multiply all the terms by the denominator
8x*x-21*x+9=0
We add all the numbers together, and all the variables
-21x+8x*x+9=0
Wy multiply elements
8x^2-21x+9=0
a = 8; b = -21; c = +9;
Δ = b2-4ac
Δ = -212-4·8·9
Δ = 153
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{17}}{2*8}=\frac{21-3\sqrt{17}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{17}}{2*8}=\frac{21+3\sqrt{17}}{16} $
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