3/4X-5/8y=1/2

Solution for 3/4X-5/8y=1/2 equation:

3/4X-5/8X=1/2

We move all terms to the left:

3/4X-5/8X-(1/2)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R



Domain of the equation: 8X!=0

X!=0/8

X!=0

X∈R


We add all the numbers together, and all the variables

3/4X-5/8X-(+1/2)=0

We get rid of parentheses

3/4X-5/8X-1/2=0

We calculate fractions


(-256X^2)/128X^2+96X/128X^2+(-80X)/128X^2=0

We multiply all the terms by the denominator


(-256X^2)+96X+(-80X)=0

We get rid of parentheses

-256X^2+96X-80X=0

We add all the numbers together, and all the variables

-256X^2+16X=0

a = -256; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-256)·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*-256}=\frac{-32}{-512}
=1/16
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-256}=\frac{0}{-512}
=0
$