0.02x+1/10x-1=0.15-0.04

Solution for 0.02x+1/10x-1=0.15-0.04 equation:

0.02x+1/10x-1=0.15-0.04

We move all terms to the left:

0.02x+1/10x-1-(0.15-0.04)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

0.02x+1/10x-1-(0.11)=0

We add all the numbers together, and all the variables

0.02x+1/10x-1.11=0

We multiply all the terms by the denominator


(0.02x)*10x-(1.11)*10x+1=0

We add all the numbers together, and all the variables

(+0.02x)*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}
$