2/3x+12-x=-20

Solution for 2/3x+12-x=-20 equation:

2/3x+12-x=-20

We move all terms to the left:

2/3x+12-x-(-20)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+2/3x+32=0

We multiply all the terms by the denominator


-1x*3x+32*3x+2=0

Wy multiply elements

-3x^2+96x+2=0

a = -3; b = 96; c = +2;
Δ = b2-4ac
Δ = 962-4·(-3)·2
Δ = 9240
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:

$\sqrt{\Delta}=\sqrt{9240}=\sqrt{4*2310}=\sqrt{4}*\sqrt{2310}=2\sqrt{2310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-2\sqrt{2310}}{2*-3}=\frac{-96-2\sqrt{2310}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+2\sqrt{2310}}{2*-3}=\frac{-96+2\sqrt{2310}}{-6}
$