5/2x+3=-x-3

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

5/2x+3=-x-3

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-(-1x-3)+3=0

We get rid of parentheses

5/2x+1x+3+3=0

We multiply all the terms by the denominator


1x*2x+3*2x+3*2x+5=0

Wy multiply elements

2x^2+6x+6x+5=0

We add all the numbers together, and all the variables

2x^2+12x+5=0

a = 2; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·2·5
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{26}}{2*2}=\frac{-12-2\sqrt{26}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{26}}{2*2}=\frac{-12+2\sqrt{26}}{4}
$