2x+7=-1/2x-3

Solution for 2x+7=-1/2x-3 equation:

2x+7=-1/2x-3

We move all terms to the left:

2x+7-(-1/2x-3)=0


Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

2x+1/2x+3+7=0

We multiply all the terms by the denominator


2x*2x+3*2x+7*2x+1=0

Wy multiply elements

4x^2+6x+14x+1=0

We add all the numbers together, and all the variables

4x^2+20x+1=0

a = 4; b = 20; c = +1;
Δ = b2-4ac
Δ = 202-4·4·1
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{6}}{2*4}=\frac{-20-8\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{6}}{2*4}=\frac{-20+8\sqrt{6}}{8}
$