(4/5)x+(1/5)x=x+1

Solution for (4/5)x+(1/5)x=x+1 equation:

(4/5)x+(1/5)x=x+1

We move all terms to the left:

(4/5)x+(1/5)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

(+4/5)x+(+1/5)x-(x+1)=0

We multiply parentheses

4x^2+x^2-(x+1)=0

We get rid of parentheses

4x^2+x^2-x-1=0

We add all the numbers together, and all the variables

5x^2-1x-1=0

a = 5; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·5·(-1)
Δ = 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{-(-1)-\sqrt{21}}{2*5}=\frac{1-\sqrt{21}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{21}}{2*5}=\frac{1+\sqrt{21}}{10}
$