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x-10/x=0.4
We move all terms to the left:
x-10/x-(0.4)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
x-10/x-0.4=0
We multiply all the terms by the denominator
x*x-(0.4)*x-10=0
We multiply parentheses
x*x-0.4x-10=0
Wy multiply elements
x^2-0.4x-10=0
a = 1; b = -0.4; c = -10;
Δ = b2-4ac
Δ = -0.42-4·1·(-10)
Δ = 40.16
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{-(-0.4)-\sqrt{40.16}}{2*1}=\frac{0.4-\sqrt{40.16}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.4)+\sqrt{40.16}}{2*1}=\frac{0.4+\sqrt{40.16}}{2} $
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