2/3y-5/4y+8=-11/12-4

Solution for 2/3y-5/4y+8=-11/12-4 equation:

2/3y-5/4y+8=-11/12-4

We move all terms to the left:

2/3y-5/4y+8-(-11/12-4)=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 get rid of parentheses

2/3y-5/4y+8+4+11/12=0

We calculate fractions


528y^2/144y^2+96y/144y^2+(-180y)/144y^2+8+4=0

We add all the numbers together, and all the variables

528y^2/144y^2+96y/144y^2+(-180y)/144y^2+12=0

We multiply all the terms by the denominator


528y^2+96y+(-180y)+12*144y^2=0

Wy multiply elements

528y^2+1728y^2+96y+(-180y)=0

We get rid of parentheses

528y^2+1728y^2+96y-180y=0

We add all the numbers together, and all the variables

2256y^2-84y=0

a = 2256; b = -84; c = 0;
Δ = b2-4ac
Δ = -842-4·2256·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-84}{2*2256}=\frac{0}{4512}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+84}{2*2256}=\frac{168}{4512}
=7/188
$