-3x-8=1/2x+6

Solution for -3x-8=1/2x+6 equation:

-3x-8=1/2x+6

We move all terms to the left:

-3x-8-(1/2x+6)=0


Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

-3x-1/2x-6-8=0

We multiply all the terms by the denominator


-3x*2x-6*2x-8*2x-1=0

Wy multiply elements

-6x^2-12x-16x-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}
$