6/5x+17=3/4x+8

Solution for 6/5x+17=3/4x+8 equation:

6/5x+17=3/4x+8

We move all terms to the left:

6/5x+17-(3/4x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x+8)!=0

x∈R


We get rid of parentheses

6/5x-3/4x-8+17=0

We calculate fractions


24x/20x^2+(-15x)/20x^2-8+17=0

We add all the numbers together, and all the variables

24x/20x^2+(-15x)/20x^2+9=0

We multiply all the terms by the denominator


24x+(-15x)+9*20x^2=0

Wy multiply elements

180x^2+24x+(-15x)=0

We get rid of parentheses

180x^2+24x-15x=0

We add all the numbers together, and all the variables

180x^2+9x=0

a = 180; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·180·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*180}=\frac{-18}{360}
=-1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*180}=\frac{0}{360}
=0
$