X=3/2y-1

Solution for X=3/2y-1 equation:

X=3/2X-1

We move all terms to the left:

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


Domain of the equation: 2X-1)!=0

X∈R


We get rid of parentheses

X-3/2X+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

2X^2+2X-3=0

a = 2; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·2·(-3)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*2}=\frac{-2-2\sqrt{7}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*2}=\frac{-2+2\sqrt{7}}{4}
$