1/2y+14=y-8

Solution for 1/2y+14=y-8 equation:

1/2y+14=y-8

We move all terms to the left:

1/2y+14-(y-8)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

1/2y-y+8+14=0

We multiply all the terms by the denominator


-y*2y+8*2y+14*2y+1=0

Wy multiply elements

-2y^2+16y+28y+1=0

We add all the numbers together, and all the variables

-2y^2+44y+1=0

a = -2; b = 44; c = +1;
Δ = b2-4ac
Δ = 442-4·(-2)·1
Δ = 1944
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:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-18\sqrt{6}}{2*-2}=\frac{-44-18\sqrt{6}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+18\sqrt{6}}{2*-2}=\frac{-44+18\sqrt{6}}{-4}
$