7/12y+15=y

Solution for 7/12y+15=y equation:

7/12y+15=y

We move all terms to the left:

7/12y+15-(y)=0


Domain of the equation: 12y!=0

y!=0/12

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+7/12y+15=0

We multiply all the terms by the denominator


-1y*12y+15*12y+7=0

Wy multiply elements

-12y^2+180y+7=0

a = -12; b = 180; c = +7;
Δ = b2-4ac
Δ = 1802-4·(-12)·7
Δ = 32736
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:

$\sqrt{\Delta}=\sqrt{32736}=\sqrt{16*2046}=\sqrt{16}*\sqrt{2046}=4\sqrt{2046}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-4\sqrt{2046}}{2*-12}=\frac{-180-4\sqrt{2046}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+4\sqrt{2046}}{2*-12}=\frac{-180+4\sqrt{2046}}{-24}
$