Y=3x-3/2x-2

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

=3Y-3/2Y-2

We move all terms to the left:

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


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

Y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6Y^2+4Y+3=0

a = -6; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·(-6)·3
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{22}}{2*-6}=\frac{-4-2\sqrt{22}}{-12}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{22}}{2*-6}=\frac{-4+2\sqrt{22}}{-12}
$