-2/3y-5/6=1/2y-7

Solution for -2/3y-5/6=1/2y-7 equation:

-2/3y-5/6=1/2y-7

We move all terms to the left:

-2/3y-5/6-(1/2y-7)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 2y-7)!=0

y∈R


We get rid of parentheses

-2/3y-1/2y+7-5/6=0

We calculate fractions


(-60y^2)/216y^2+(-144y)/216y^2+(-108y)/216y^2+7=0

We multiply all the terms by the denominator


(-60y^2)+(-144y)+(-108y)+7*216y^2=0

Wy multiply elements

(-60y^2)+1512y^2+(-144y)+(-108y)=0

We get rid of parentheses

-60y^2+1512y^2-144y-108y=0

We add all the numbers together, and all the variables

1452y^2-252y=0

a = 1452; b = -252; c = 0;
Δ = b2-4ac
Δ = -2522-4·1452·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-252}{2*1452}=\frac{0}{2904}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+252}{2*1452}=\frac{504}{2904}
=21/121
$