13/8x+7/2=9/4x+9

Solution for 13/8x+7/2=9/4x+9 equation:

13/8x+7/2=9/4x+9

We move all terms to the left:

13/8x+7/2-(9/4x+9)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x+9)!=0

x∈R


We get rid of parentheses

13/8x-9/4x-9+7/2=0

We calculate fractions


896x^2/128x^2+208x/128x^2+(-288x)/128x^2-9=0

We multiply all the terms by the denominator


896x^2+208x+(-288x)-9*128x^2=0

Wy multiply elements

896x^2-1152x^2+208x+(-288x)=0

We get rid of parentheses

896x^2-1152x^2+208x-288x=0

We add all the numbers together, and all the variables

-256x^2-80x=0

a = -256; b = -80; c = 0;
Δ = b2-4ac
Δ = -802-4·(-256)·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-80}{2*-256}=\frac{0}{-512}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+80}{2*-256}=\frac{160}{-512}
=-5/16
$