7/8x+9/2=1/4x

Solution for 7/8x+9/2=1/4x equation:

7/8x+9/2=1/4x

We move all terms to the left:

7/8x+9/2-(1/4x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7/8x-(+1/4x)+9/2=0

We get rid of parentheses

7/8x-1/4x+9/2=0

We calculate fractions


1152x^2/128x^2+112x/128x^2+(-32x)/128x^2=0

We multiply all the terms by the denominator


1152x^2+112x+(-32x)=0

We get rid of parentheses

1152x^2+112x-32x=0

We add all the numbers together, and all the variables

1152x^2+80x=0

a = 1152; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·1152·0
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*1152}=\frac{-160}{2304}
=-5/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*1152}=\frac{0}{2304}
=0
$