3/2x-7=6x+18

Solution for 3/2x-7=6x+18 equation:

3/2x-7=6x+18

We move all terms to the left:

3/2x-7-(6x+18)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-6x-18-7=0

We multiply all the terms by the denominator


-6x*2x-18*2x-7*2x+3=0

Wy multiply elements

-12x^2-36x-14x+3=0

We add all the numbers together, and all the variables

-12x^2-50x+3=0

a = -12; b = -50; c = +3;
Δ = b2-4ac
Δ = -502-4·(-12)·3
Δ = 2644
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:

$\sqrt{\Delta}=\sqrt{2644}=\sqrt{4*661}=\sqrt{4}*\sqrt{661}=2\sqrt{661}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{661}}{2*-12}=\frac{50-2\sqrt{661}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{661}}{2*-12}=\frac{50+2\sqrt{661}}{-24}
$