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0=10/x-5-7x
We move all terms to the left:
0-(10/x-5-7x)=0
Domain of the equation: x-5-7x)!=0We add all the numbers together, and all the variables
We move all terms containing x to the left, all other terms to the right
x-7x)!=5
x∈R
-(-7x+10/x-5)+0=0
We add all the numbers together, and all the variables
-(-7x+10/x-5)=0
We get rid of parentheses
7x-10/x+5=0
We multiply all the terms by the denominator
7x*x+5*x-10=0
We add all the numbers together, and all the variables
5x+7x*x-10=0
Wy multiply elements
7x^2+5x-10=0
a = 7; b = 5; c = -10;
Δ = b2-4ac
Δ = 52-4·7·(-10)
Δ = 305
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{-(5)-\sqrt{305}}{2*7}=\frac{-5-\sqrt{305}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{305}}{2*7}=\frac{-5+\sqrt{305}}{14} $
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