1/5x-0.5=x+3.25

Solution for 1/5x-0.5=x+3.25 equation:

1/5x-0.5=x+3.25

We move all terms to the left:

1/5x-0.5-(x+3.25)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-x-3.25-0.5=0

We multiply all the terms by the denominator


-x*5x-(3.25)*5x-(0.5)*5x+1=0

We multiply parentheses

-x*5x-16.25x-2.5x+1=0

Wy multiply elements

-5x^2-16.25x-2.5x+1=0

We add all the numbers together, and all the variables

-5x^2-18.75x+1=0

a = -5; b = -18.75; c = +1;
Δ = b2-4ac
Δ = -18.752-4·(-5)·1
Δ = 371.5625
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{-(-18.75)-\sqrt{371.5625}}{2*-5}=\frac{18.75-\sqrt{371.5625}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18.75)+\sqrt{371.5625}}{2*-5}=\frac{18.75+\sqrt{371.5625}}{-10}
$