3/2x-2=5x+8

Solution for 3/2x-2=5x+8 equation:

3/2x-2=5x+8

We move all terms to the left:

3/2x-2-(5x+8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-5x-8-2=0

We multiply all the terms by the denominator


-5x*2x-8*2x-2*2x+3=0

Wy multiply elements

-10x^2-16x-4x+3=0

We add all the numbers together, and all the variables

-10x^2-20x+3=0

a = -10; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·(-10)·3
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{130}}{2*-10}=\frac{20-2\sqrt{130}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{130}}{2*-10}=\frac{20+2\sqrt{130}}{-20}
$