1/2y+3y-12=30

Solution for 1/2y+3y-12=30 equation:

1/2y+3y-12=30

We move all terms to the left:

1/2y+3y-12-(30)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

3y+1/2y-42=0

We multiply all the terms by the denominator


3y*2y-42*2y+1=0

Wy multiply elements

6y^2-84y+1=0

a = 6; b = -84; c = +1;
Δ = b2-4ac
Δ = -842-4·6·1
Δ = 7032
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:

$\sqrt{\Delta}=\sqrt{7032}=\sqrt{4*1758}=\sqrt{4}*\sqrt{1758}=2\sqrt{1758}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1758}}{2*6}=\frac{84-2\sqrt{1758}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1758}}{2*6}=\frac{84+2\sqrt{1758}}{12}
$