4/5x+4.5=x

Solution for 4/5x+4.5=x equation:

4/5x+4.5=x

We move all terms to the left:

4/5x+4.5-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4/5x+4.5=0

We multiply all the terms by the denominator


-1x*5x+(4.5)*5x+4=0

We multiply parentheses

-1x*5x+22.5x+4=0

Wy multiply elements

-5x^2+22.5x+4=0

a = -5; b = 22.5; c = +4;
Δ = b2-4ac
Δ = 22.52-4·(-5)·4
Δ = 586.25
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{-(22.5)-\sqrt{586.25}}{2*-5}=\frac{-22.5-\sqrt{586.25}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22.5)+\sqrt{586.25}}{2*-5}=\frac{-22.5+\sqrt{586.25}}{-10}
$