1/2y+3=y-33

Solution for 1/2y+3=y-33 equation:

1/2y+3=y-33

We move all terms to the left:

1/2y+3-(y-33)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

1/2y-y+33+3=0

We multiply all the terms by the denominator


-y*2y+33*2y+3*2y+1=0

Wy multiply elements

-2y^2+66y+6y+1=0

We add all the numbers together, and all the variables

-2y^2+72y+1=0

a = -2; b = 72; c = +1;
Δ = b2-4ac
Δ = 722-4·(-2)·1
Δ = 5192
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:

$\sqrt{\Delta}=\sqrt{5192}=\sqrt{4*1298}=\sqrt{4}*\sqrt{1298}=2\sqrt{1298}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1298}}{2*-2}=\frac{-72-2\sqrt{1298}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1298}}{2*-2}=\frac{-72+2\sqrt{1298}}{-4}
$