-7/3(y)-5/4=7/4(y)-7

Solution for -7/3(y)-5/4=7/4(y)-7 equation:

-7/3(y)-5/4=7/4(y)-7

We move all terms to the left:

-7/3(y)-5/4-(7/4(y)-7)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 4y-7)!=0

y∈R


We get rid of parentheses

-7/3y-7/4y+7-5/4=0

We calculate fractions


(-448y)/192y^2+(-21y)/192y^2+(-15y)/192y^2+7=0

We multiply all the terms by the denominator


(-448y)+(-21y)+(-15y)+7*192y^2=0

Wy multiply elements

1344y^2+(-448y)+(-21y)+(-15y)=0

We get rid of parentheses

1344y^2-448y-21y-15y=0

We add all the numbers together, and all the variables

1344y^2-484y=0

a = 1344; b = -484; c = 0;
Δ = b2-4ac
Δ = -4842-4·1344·0
Δ = 234256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{234256}=484$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-484)-484}{2*1344}=\frac{0}{2688}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-484)+484}{2*1344}=\frac{968}{2688}
=121/336
$