3/2x+8=3x-3

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

3/2x+8=3x-3

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+6x+16x+3=0

We add all the numbers together, and all the variables

-6x^2+22x+3=0

a = -6; b = 22; c = +3;
Δ = b2-4ac
Δ = 222-4·(-6)·3
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{139}}{2*-6}=\frac{-22-2\sqrt{139}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{139}}{2*-6}=\frac{-22+2\sqrt{139}}{-12}
$