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0.2x+1/10x-1=0.15-0.04
We move all terms to the left:
0.2x+1/10x-1-(0.15-0.04)=0
Domain of the equation: 10x!=0We add all the numbers together, and all the variables
x!=0/10
x!=0
x∈R
0.2x+1/10x-1-(0.11)=0
We add all the numbers together, and all the variables
0.2x+1/10x-1.11=0
We multiply all the terms by the denominator
(0.2x)*10x-(1.11)*10x+1=0
We add all the numbers together, and all the variables
(+0.2x)*10x-(1.11)*10x+1=0
We multiply parentheses
0x^2-11.1x+1=0
We add all the numbers together, and all the variables
x^2-11.1x+1=0
a = 1; b = -11.1; c = +1;
Δ = b2-4ac
Δ = -11.12-4·1·1
Δ = 119.21
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{-(-11.1)-\sqrt{119.21}}{2*1}=\frac{11.1-\sqrt{119.21}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11.1)+\sqrt{119.21}}{2*1}=\frac{11.1+\sqrt{119.21}}{2} $
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