-3/2x+7=3x-2

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

-3/2x+7=3x-2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+4x+14x-3=0

We add all the numbers together, and all the variables

-6x^2+18x-3=0

a = -6; b = 18; c = -3;
Δ = b2-4ac
Δ = 182-4·(-6)·(-3)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{7}}{2*-6}=\frac{-18-6\sqrt{7}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{7}}{2*-6}=\frac{-18+6\sqrt{7}}{-12}
$