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

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

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

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We calculate fractions


(-8y)/12y^2+(-9y)/12y^2-5=0

We multiply all the terms by the denominator


(-8y)+(-9y)-5*12y^2=0

Wy multiply elements

-60y^2+(-8y)+(-9y)=0

We get rid of parentheses

-60y^2-8y-9y=0

We add all the numbers together, and all the variables

-60y^2-17y=0

a = -60; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·(-60)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*-60}=\frac{0}{-120}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*-60}=\frac{34}{-120}
=-17/60
$