x=-2/3x-4

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

x=-2/3x-4

We move all terms to the left:

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


Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

x+2/3x+4=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+12x+2=0

a = 3; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·3·2
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{30}}{2*3}=\frac{-12-2\sqrt{30}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{30}}{2*3}=\frac{-12+2\sqrt{30}}{6}
$