-x-4=7/3x+6

Solution for -x-4=7/3x+6 equation:

-x-4=7/3x+6

We move all terms to the left:

-x-4-(7/3x+6)=0


Domain of the equation: 3x+6)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(7/3x+6)-4=0

We get rid of parentheses

-1x-7/3x-6-4=0

We multiply all the terms by the denominator


-1x*3x-6*3x-4*3x-7=0

Wy multiply elements

-3x^2-18x-12x-7=0

We add all the numbers together, and all the variables

-3x^2-30x-7=0

a = -3; b = -30; c = -7;
Δ = b2-4ac
Δ = -302-4·(-3)·(-7)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4\sqrt{51}}{2*-3}=\frac{30-4\sqrt{51}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4\sqrt{51}}{2*-3}=\frac{30+4\sqrt{51}}{-6}
$