6y-8=2/3y-4

Solution for 6y-8=2/3y-4 equation:

6y-8=2/3y-4

We move all terms to the left:

6y-8-(2/3y-4)=0


Domain of the equation: 3y-4)!=0

y∈R


We get rid of parentheses

6y-2/3y+4-8=0

We multiply all the terms by the denominator


6y*3y+4*3y-8*3y-2=0

Wy multiply elements

18y^2+12y-24y-2=0

We add all the numbers together, and all the variables

18y^2-12y-2=0

a = 18; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·18·(-2)
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{2}}{2*18}=\frac{12-12\sqrt{2}}{36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{2}}{2*18}=\frac{12+12\sqrt{2}}{36}
$