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2x-17/x+4=7
We move all terms to the left:
2x-17/x+4-(7)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
2x-17/x-3=0
We multiply all the terms by the denominator
2x*x-3*x-17=0
We add all the numbers together, and all the variables
-3x+2x*x-17=0
Wy multiply elements
2x^2-3x-17=0
a = 2; b = -3; c = -17;
Δ = b2-4ac
Δ = -32-4·2·(-17)
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{-(-3)-\sqrt{145}}{2*2}=\frac{3-\sqrt{145}}{4}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{145}}{2*2}=\frac{3+\sqrt{145}}{4}
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