1/2x+4=-3x-10

Solution for 1/2x+4=-3x-10 equation:

1/2x+4=-3x-10

We move all terms to the left:

1/2x+4-(-3x-10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x+3x+10+4=0

We multiply all the terms by the denominator


3x*2x+10*2x+4*2x+1=0

Wy multiply elements

6x^2+20x+8x+1=0

We add all the numbers together, and all the variables

6x^2+28x+1=0

a = 6; b = 28; c = +1;
Δ = b2-4ac
Δ = 282-4·6·1
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{190}}{2*6}=\frac{-28-2\sqrt{190}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{190}}{2*6}=\frac{-28+2\sqrt{190}}{12}
$