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

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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} $

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