X-0,1=1/2x+0,05

Solution for X-0,1=1/2x+0,05 equation:

X-0.1=1/2X+0.05

We move all terms to the left:

X-0.1-(1/2X+0.05)=0


Domain of the equation: 2X+0.05)!=0

X∈R


We get rid of parentheses

X-1/2X-0.05-0.1=0

We multiply all the terms by the denominator


X*2X-(0.05)*2X-(0.1)*2X-1=0

We multiply parentheses

X*2X-0.1X-0.2X-1=0

Wy multiply elements

2X^2-0.1X-0.2X-1=0

We add all the numbers together, and all the variables

2X^2-0.3X-1=0

a = 2; b = -0.3; c = -1;
Δ = b2-4ac
Δ = -0.32-4·2·(-1)
Δ = 8.09
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{-(-0.3)-\sqrt{8.09}}{2*2}=\frac{0.3-\sqrt{8.09}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.3)+\sqrt{8.09}}{2*2}=\frac{0.3+\sqrt{8.09}}{4}
$