3/2x+20=2x-32

Solution for 3/2x+20=2x-32 equation:

3/2x+20=2x-32

We move all terms to the left:

3/2x+20-(2x-32)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-2x+32+20=0

We multiply all the terms by the denominator


-2x*2x+32*2x+20*2x+3=0

Wy multiply elements

-4x^2+64x+40x+3=0

We add all the numbers together, and all the variables

-4x^2+104x+3=0

a = -4; b = 104; c = +3;
Δ = b2-4ac
Δ = 1042-4·(-4)·3
Δ = 10864
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:

$\sqrt{\Delta}=\sqrt{10864}=\sqrt{16*679}=\sqrt{16}*\sqrt{679}=4\sqrt{679}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-4\sqrt{679}}{2*-4}=\frac{-104-4\sqrt{679}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+4\sqrt{679}}{2*-4}=\frac{-104+4\sqrt{679}}{-8}
$