1/3x+1=-0,25x+2

Solution for 1/3x+1=-0,25x+2 equation:

1/3x+1=-0.25x+2

We move all terms to the left:

1/3x+1-(-0.25x+2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x+0.25x-2+1=0

We multiply all the terms by the denominator


(0.25x)*3x-2*3x+1*3x+1=0

We add all the numbers together, and all the variables

(+0.25x)*3x-2*3x+1*3x+1=0

We multiply parentheses

0x^2-2*3x+1*3x+1=0

Wy multiply elements

0x^2-6x+3x+1=0

We add all the numbers together, and all the variables

x^2-3x+1=0

a = 1; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·1·1
Δ = 5
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{-(-3)-\sqrt{5}}{2*1}=\frac{3-\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{5}}{2*1}=\frac{3+\sqrt{5}}{2}
$