-4x=2/3x-14

Solution for -4x=2/3x-14 equation:

-4x=2/3x-14

We move all terms to the left:

-4x-(2/3x-14)=0


Domain of the equation: 3x-14)!=0

x∈R


We get rid of parentheses

-4x-2/3x+14=0

We multiply all the terms by the denominator


-4x*3x+14*3x-2=0

Wy multiply elements

-12x^2+42x-2=0

a = -12; b = 42; c = -2;
Δ = b2-4ac
Δ = 422-4·(-12)·(-2)
Δ = 1668
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:

$\sqrt{\Delta}=\sqrt{1668}=\sqrt{4*417}=\sqrt{4}*\sqrt{417}=2\sqrt{417}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{417}}{2*-12}=\frac{-42-2\sqrt{417}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{417}}{2*-12}=\frac{-42+2\sqrt{417}}{-24}
$