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2x+-1/5x+3=-8
We move all terms to the left:
2x+-1/5x+3-(-8)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
2x-1/5x+11=0
We multiply all the terms by the denominator
2x*5x+11*5x-1=0
Wy multiply elements
10x^2+55x-1=0
a = 10; b = 55; c = -1;
Δ = b2-4ac
Δ = 552-4·10·(-1)
Δ = 3065
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{-(55)-\sqrt{3065}}{2*10}=\frac{-55-\sqrt{3065}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{3065}}{2*10}=\frac{-55+\sqrt{3065}}{20} $
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