Y=3x-7/2x

Solution for Y=3x-7/2x equation:

=3Y-7/2Y

We move all terms to the left:

-(3Y-7/2Y)=0


Domain of the equation: 2Y)!=0

Y!=0/1

Y!=0

Y∈R


We add all the numbers together, and all the variables

-(+3Y-7/2Y)=0

We get rid of parentheses

-3Y+7/2Y=0

We multiply all the terms by the denominator


-3Y*2Y+7=0

Wy multiply elements

-6Y^2+7=0

a = -6; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-6)·7
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*-6}=\frac{0-2\sqrt{42}}{-12}
=-\frac{2\sqrt{42}}{-12}
=-\frac{\sqrt{42}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*-6}=\frac{0+2\sqrt{42}}{-12}
=\frac{2\sqrt{42}}{-12}
=\frac{\sqrt{42}}{-6}
$