3/2x-2=-2x+5

Solution for 3/2x-2=-2x+5 equation:

3/2x-2=-2x+5

We move all terms to the left:

3/2x-2-(-2x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x+2x-5-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-10x-4x+3=0

We add all the numbers together, and all the variables

4x^2-14x+3=0

a = 4; b = -14; c = +3;
Δ = b2-4ac
Δ = -142-4·4·3
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{37}}{2*4}=\frac{14-2\sqrt{37}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{37}}{2*4}=\frac{14+2\sqrt{37}}{8}
$