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!=0/5

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


-(1.5x)*5x-29*5x+8*5x+4=0

We add all the numbers together, and all the variables

-(+1.5x)*5x-29*5x+8*5x+4=0

We multiply parentheses

-5x^2-29*5x+8*5x+4=0

Wy multiply elements

-5x^2-145x+40x+4=0

We add all the numbers together, and all the variables

-5x^2-105x+4=0

a = -5; b = -105; c = +4;
Δ = b2-4ac
Δ = -1052-4·(-5)·4
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*-5}=\frac{105-\sqrt{11105}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{11105}}{2*-5}=\frac{105+\sqrt{11105}}{-10}
$