Y=3x-2/2x+1

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

=3Y-2/2Y+1

We move all terms to the left:

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


Domain of the equation: 2Y+1)!=0

Y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-3Y*2Y-1*2Y+2=0

Wy multiply elements

-6Y^2-2Y+2=0

a = -6; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-6)·2
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{13}}{2*-6}=\frac{2-2\sqrt{13}}{-12}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{13}}{2*-6}=\frac{2+2\sqrt{13}}{-12}
$