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

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

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

We move all terms to the left:

-5/4y-1/4-(2/3y-2)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 3y-2)!=0

y∈R


We get rid of parentheses

-5/4y-2/3y+2-1/4=0

We calculate fractions


(-15y)/192y^2+(-128y)/192y^2+(-3y)/192y^2+2=0

We multiply all the terms by the denominator


(-15y)+(-128y)+(-3y)+2*192y^2=0

Wy multiply elements

384y^2+(-15y)+(-128y)+(-3y)=0

We get rid of parentheses

384y^2-15y-128y-3y=0

We add all the numbers together, and all the variables

384y^2-146y=0

a = 384; b = -146; c = 0;
Δ = b2-4ac
Δ = -1462-4·384·0
Δ = 21316
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21316}=146$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-146)-146}{2*384}=\frac{0}{768}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-146)+146}{2*384}=\frac{292}{768}
=73/192
$