7/8x-5/2=3/4x

Solution for 7/8x-5/2=3/4x equation:

7/8x-5/2=3/4x

We move all terms to the left:

7/8x-5/2-(3/4x)=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-(+3/4x)-5/2=0

We get rid of parentheses

7/8x-3/4x-5/2=0

We calculate fractions


(-640x^2)/128x^2+112x/128x^2+(-96x)/128x^2=0

We multiply all the terms by the denominator


(-640x^2)+112x+(-96x)=0

We get rid of parentheses

-640x^2+112x-96x=0

We add all the numbers together, and all the variables

-640x^2+16x=0

a = -640; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-640)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-640}=\frac{-32}{-1280}
=1/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-640}=\frac{0}{-1280}
=0
$