Y=1/2x-3;x=-2

Solution for Y=1/2x-3;x=-2 equation:

=1/2Y-3Y=-2

We move all terms to the left:

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


Domain of the equation: 2Y-3Y)!=0

Y∈R


We add all the numbers together, and all the variables

-(-3Y+1/2Y)=0

We get rid of parentheses

3Y-1/2Y=0

We multiply all the terms by the denominator


3Y*2Y-1=0

Wy multiply elements

6Y^2-1=0

a = 6; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·6·(-1)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*6}=\frac{0-2\sqrt{6}}{12}
=-\frac{2\sqrt{6}}{12}
=-\frac{\sqrt{6}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*6}=\frac{0+2\sqrt{6}}{12}
=\frac{2\sqrt{6}}{12}
=\frac{\sqrt{6}}{6}
$