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x+35/x=-12
We move all terms to the left:
x+35/x-(-12)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
x+35/x+12=0
We multiply all the terms by the denominator
x*x+12*x+35=0
We add all the numbers together, and all the variables
12x+x*x+35=0
Wy multiply elements
x^2+12x+35=0
a = 1; b = 12; c = +35;
Δ = b2-4ac
Δ = 122-4·1·35
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2}{2*1}=\frac{-14}{2} =-7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2}{2*1}=\frac{-10}{2} =-5 $
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