4/5x-4+.5x=1

Solution for 4/5x-4+.5x=1 equation:

4/5x-4+.5x=1

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

.5x+4/5x-5=0

We multiply all the terms by the denominator


(.5x)*5x-5*5x+4=0

We add all the numbers together, and all the variables

(+.5x)*5x-5*5x+4=0

We multiply parentheses

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

Wy multiply elements

5x^2-25x+4=0

a = 5; b = -25; c = +4;
Δ = b2-4ac
Δ = -252-4·5·4
Δ = 545
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{-(-25)-\sqrt{545}}{2*5}=\frac{25-\sqrt{545}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{545}}{2*5}=\frac{25+\sqrt{545}}{10}
$