(1/5)+(2/5)x=x+1

Solution for (1/5)+(2/5)x=x+1 equation:

(1/5)+(2/5)x=x+1

We move all terms to the left:

(1/5)+(2/5)x-(x+1)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/5)x-(x+1)+(+1/5)=0

We multiply parentheses

2x^2-(x+1)+(+1/5)=0

We get rid of parentheses

2x^2-x-1+1/5=0

We multiply all the terms by the denominator


2x^2*5-x*5+1-1*5=0

We add all the numbers together, and all the variables

2x^2*5-x*5-4=0

Wy multiply elements

10x^2-5x-4=0

a = 10; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·10·(-4)
Δ = 185
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{-(-5)-\sqrt{185}}{2*10}=\frac{5-\sqrt{185}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{185}}{2*10}=\frac{5+\sqrt{185}}{20}
$