-1/2y-3y=-2-(8-5)

Solution for -1/2y-3y=-2-(8-5) equation:

-1/2y-3y=-2-(8-5)

We move all terms to the left:

-1/2y-3y-(-2-(8-5))=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-3y-1/2y+5=0

We multiply all the terms by the denominator


-3y*2y+5*2y-1=0

Wy multiply elements

-6y^2+10y-1=0

a = -6; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·(-6)·(-1)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{19}}{2*-6}=\frac{-10-2\sqrt{19}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{19}}{2*-6}=\frac{-10+2\sqrt{19}}{-12}
$