3/2x+5=-2x-9

Solution for 3/2x+5=-2x-9 equation:

3/2x+5=-2x-9

We move all terms to the left:

3/2x+5-(-2x-9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x+2x+9+5=0

We multiply all the terms by the denominator


2x*2x+9*2x+5*2x+3=0

Wy multiply elements

4x^2+18x+10x+3=0

We add all the numbers together, and all the variables

4x^2+28x+3=0

a = 4; b = 28; c = +3;
Δ = b2-4ac
Δ = 282-4·4·3
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{46}}{2*4}=\frac{-28-4\sqrt{46}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{46}}{2*4}=\frac{-28+4\sqrt{46}}{8}
$