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1/x-1=7/2x+5
We move all terms to the left:
1/x-1-(7/2x+5)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 2x+5)!=0We get rid of parentheses
x∈R
1/x-7/2x-5-1=0
We calculate fractions
2x/2x^2+(-7x)/2x^2-5-1=0
We add all the numbers together, and all the variables
2x/2x^2+(-7x)/2x^2-6=0
We multiply all the terms by the denominator
2x+(-7x)-6*2x^2=0
Wy multiply elements
-12x^2+2x+(-7x)=0
We get rid of parentheses
-12x^2+2x-7x=0
We add all the numbers together, and all the variables
-12x^2-5x=0
a = -12; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-12)·0
Δ = 25
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-12}=\frac{0}{-24} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-12}=\frac{10}{-24} =-5/12 $
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