-3x-14=1/2x

Solution for -3x-14=1/2x equation:

-3x-14=1/2x

We move all terms to the left:

-3x-14-(1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3x-(+1/2x)-14=0

We get rid of parentheses

-3x-1/2x-14=0

We multiply all the terms by the denominator


-3x*2x-14*2x-1=0

Wy multiply elements

-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}
$