2x-7=3/2x

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

2x-7=3/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x-3/2x-7=0

We multiply all the terms by the denominator


2x*2x-7*2x-3=0

Wy multiply elements

4x^2-14x-3=0

a = 4; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·4·(-3)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{61}}{2*4}=\frac{14-2\sqrt{61}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{61}}{2*4}=\frac{14+2\sqrt{61}}{8}
$