-3/2x=-36+3x

Solution for -3/2x=-36+3x equation:

-3/2x=-36+3x

We move all terms to the left:

-3/2x-(-36+3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-3/2x-(3x-36)=0

We get rid of parentheses

-3/2x-3x+36=0

We multiply all the terms by the denominator


-3x*2x+36*2x-3=0

Wy multiply elements

-6x^2+72x-3=0

a = -6; b = 72; c = -3;
Δ = b2-4ac
Δ = 722-4·(-6)·(-3)
Δ = 5112
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:

$\sqrt{\Delta}=\sqrt{5112}=\sqrt{36*142}=\sqrt{36}*\sqrt{142}=6\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-6\sqrt{142}}{2*-6}=\frac{-72-6\sqrt{142}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+6\sqrt{142}}{2*-6}=\frac{-72+6\sqrt{142}}{-12}
$