x/5x+7=9x-17

Solution for x/5x+7=9x-17 equation:

x/5x+7=9x-17

We move all terms to the left:

x/5x+7-(9x-17)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

x/5x-9x+17+7=0

We multiply all the terms by the denominator


x-9x*5x+17*5x+7*5x=0

Wy multiply elements

-45x^2+x+85x+35x=0

We add all the numbers together, and all the variables

-45x^2+121x=0

a = -45; b = 121; c = 0;
Δ = b2-4ac
Δ = 1212-4·(-45)·0
Δ = 14641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14641}=121$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(121)-121}{2*-45}=\frac{-242}{-90}
=2+31/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(121)+121}{2*-45}=\frac{0}{-90}
=0
$