-2/3x+4(3-x)=26

Solution for -2/3x+4(3-x)=26 equation:

-2/3x+4(3-x)=26

We move all terms to the left:

-2/3x+4(3-x)-(26)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-2/3x+4(-1x+3)-26=0

We multiply parentheses

-2/3x-4x+12-26=0

We multiply all the terms by the denominator


-4x*3x+12*3x-26*3x-2=0

Wy multiply elements

-12x^2+36x-78x-2=0

We add all the numbers together, and all the variables

-12x^2-42x-2=0

a = -12; b = -42; c = -2;
Δ = b2-4ac
Δ = -422-4·(-12)·(-2)
Δ = 1668
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:

$\sqrt{\Delta}=\sqrt{1668}=\sqrt{4*417}=\sqrt{4}*\sqrt{417}=2\sqrt{417}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{417}}{2*-12}=\frac{42-2\sqrt{417}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{417}}{2*-12}=\frac{42+2\sqrt{417}}{-24}
$