4.5x+8=29+1/5x

Solution for 4.5x+8=29+1/5x equation:

4.5x+8=29+1/5x

We move all terms to the left:

4.5x+8-(29+1/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4.5x-(1/5x+29)+8=0

We get rid of parentheses

4.5x-1/5x-29+8=0

We multiply all the terms by the denominator


(4.5x)*5x-29*5x+8*5x-1=0

We add all the numbers together, and all the variables

(+4.5x)*5x-29*5x+8*5x-1=0

We multiply parentheses

20x^2-29*5x+8*5x-1=0

Wy multiply elements

20x^2-145x+40x-1=0

We add all the numbers together, and all the variables

20x^2-105x-1=0

a = 20; b = -105; c = -1;
Δ = b2-4ac
Δ = -1052-4·20·(-1)
Δ = 11105
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{-(-105)-\sqrt{11105}}{2*20}=\frac{105-\sqrt{11105}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{11105}}{2*20}=\frac{105+\sqrt{11105}}{40}
$