x+7=-12/3x

Solution for x+7=-12/3x equation:

x+7=-12/3x

We move all terms to the left:

x+7-(-12/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

x+12/3x+7=0

We multiply all the terms by the denominator


x*3x+7*3x+12=0

Wy multiply elements

3x^2+21x+12=0

a = 3; b = 21; c = +12;
Δ = b2-4ac
Δ = 212-4·3·12
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{33}}{2*3}=\frac{-21-3\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{33}}{2*3}=\frac{-21+3\sqrt{33}}{6}
$