1/2y+12=y-18

Solution for 1/2y+12=y-18 equation:

1/2y+12=y-18

We move all terms to the left:

1/2y+12-(y-18)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

1/2y-y+18+12=0

We multiply all the terms by the denominator


-y*2y+18*2y+12*2y+1=0

Wy multiply elements

-2y^2+36y+24y+1=0

We add all the numbers together, and all the variables

-2y^2+60y+1=0

a = -2; b = 60; c = +1;
Δ = b2-4ac
Δ = 602-4·(-2)·1
Δ = 3608
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:

$\sqrt{\Delta}=\sqrt{3608}=\sqrt{4*902}=\sqrt{4}*\sqrt{902}=2\sqrt{902}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{902}}{2*-2}=\frac{-60-2\sqrt{902}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{902}}{2*-2}=\frac{-60+2\sqrt{902}}{-4}
$