X+4/3x=-14

Solution for X+4/3x=-14 equation:

X+4/3X=-14

We move all terms to the left:

X+4/3X-(-14)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X+4/3X+14=0

We multiply all the terms by the denominator


X*3X+14*3X+4=0

Wy multiply elements

3X^2+42X+4=0

a = 3; b = 42; c = +4;
Δ = b2-4ac
Δ = 422-4·3·4
Δ = 1716
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:

$\sqrt{\Delta}=\sqrt{1716}=\sqrt{4*429}=\sqrt{4}*\sqrt{429}=2\sqrt{429}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{429}}{2*3}=\frac{-42-2\sqrt{429}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{429}}{2*3}=\frac{-42+2\sqrt{429}}{6}
$