7/4y-6=13/8y+2

Solution for 7/4y-6=13/8y+2 equation:

7/4y-6=13/8y+2

We move all terms to the left:

7/4y-6-(13/8y+2)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 8y+2)!=0

y∈R


We get rid of parentheses

7/4y-13/8y-2-6=0

We calculate fractions


56y/32y^2+(-52y)/32y^2-2-6=0

We add all the numbers together, and all the variables

56y/32y^2+(-52y)/32y^2-8=0

We multiply all the terms by the denominator


56y+(-52y)-8*32y^2=0

Wy multiply elements

-256y^2+56y+(-52y)=0

We get rid of parentheses

-256y^2+56y-52y=0

We add all the numbers together, and all the variables

-256y^2+4y=0

a = -256; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-256)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-256}=\frac{-8}{-512}
=1/64
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-256}=\frac{0}{-512}
=0
$