X=3/2y-5

Solution for X=3/2y-5 equation:

X=3/2X-5

We move all terms to the left:

X-(3/2X-5)=0


Domain of the equation: 2X-5)!=0

X∈R


We get rid of parentheses

X-3/2X+5=0

We multiply all the terms by the denominator


X*2X+5*2X-3=0

Wy multiply elements

2X^2+10X-3=0

a = 2; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·2·(-3)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{31}}{2*2}=\frac{-10-2\sqrt{31}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{31}}{2*2}=\frac{-10+2\sqrt{31}}{4}
$