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3x+8/x-5=21
We move all terms to the left:
3x+8/x-5-(21)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
3x+8/x-26=0
We multiply all the terms by the denominator
3x*x-26*x+8=0
We add all the numbers together, and all the variables
-26x+3x*x+8=0
Wy multiply elements
3x^2-26x+8=0
a = 3; b = -26; c = +8;
Δ = b2-4ac
Δ = -262-4·3·8
Δ = 580
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{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{145}}{2*3}=\frac{26-2\sqrt{145}}{6}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{145}}{2*3}=\frac{26+2\sqrt{145}}{6}
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