x/9x+7-5x-10=29

Solution for x/9x+7-5x-10=29 equation:

x/9x+7-5x-10=29

We move all terms to the left:

x/9x+7-5x-10-(29)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

-5x+x/9x-32=0

We multiply all the terms by the denominator


-5x*9x+x-32*9x=0

We add all the numbers together, and all the variables

x-5x*9x-32*9x=0

Wy multiply elements

-45x^2+x-288x=0

We add all the numbers together, and all the variables

-45x^2-287x=0

a = -45; b = -287; c = 0;
Δ = b2-4ac
Δ = -2872-4·(-45)·0
Δ = 82369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82369}=287$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-287)-287}{2*-45}=\frac{0}{-90}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-287)+287}{2*-45}=\frac{574}{-90}
=-6+17/45
$