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

Solution for 1/2x+5=-3x+2 equation:

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-4x+10x+1=0

We add all the numbers together, and all the variables

6x^2+6x+1=0

a = 6; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·6·1
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{3}}{2*6}=\frac{-6-2\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{3}}{2*6}=\frac{-6+2\sqrt{3}}{12}
$