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1/5x+5x=17-7x
We move all terms to the left:
1/5x+5x-(17-7x)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
1/5x+5x-(-7x+17)=0
We add all the numbers together, and all the variables
5x+1/5x-(-7x+17)=0
We get rid of parentheses
5x+1/5x+7x-17=0
We multiply all the terms by the denominator
5x*5x+7x*5x-17*5x+1=0
Wy multiply elements
25x^2+35x^2-85x+1=0
We add all the numbers together, and all the variables
60x^2-85x+1=0
a = 60; b = -85; c = +1;
Δ = b2-4ac
Δ = -852-4·60·1
Δ = 6985
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{-(-85)-\sqrt{6985}}{2*60}=\frac{85-\sqrt{6985}}{120} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+\sqrt{6985}}{2*60}=\frac{85+\sqrt{6985}}{120} $
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