6-1/2y=18-3y

Solution for 6-1/2y=18-3y equation:

6-1/2y=18-3y

We move all terms to the left:

6-1/2y-(18-3y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-1/2y-(-3y+18)+6=0

We get rid of parentheses

-1/2y+3y-18+6=0

We multiply all the terms by the denominator


3y*2y-18*2y+6*2y-1=0

Wy multiply elements

6y^2-36y+12y-1=0

We add all the numbers together, and all the variables

6y^2-24y-1=0

a = 6; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·6·(-1)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-10\sqrt{6}}{2*6}=\frac{24-10\sqrt{6}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+10\sqrt{6}}{2*6}=\frac{24+10\sqrt{6}}{12}
$