3/2x-1+2x=-6

Solution for 3/2x-1+2x=-6 equation:

3/2x-1+2x=-6

We move all terms to the left:

3/2x-1+2x-(-6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+3/2x+5=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+10x+3=0

a = 4; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·4·3
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{13}}{2*4}=\frac{-10-2\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{13}}{2*4}=\frac{-10+2\sqrt{13}}{8}
$