2/3x-4(x+8)=3-10x

Solution for 2/3x-4(x+8)=3-10x equation:

2/3x-4(x+8)=3-10x

We move all terms to the left:

2/3x-4(x+8)-(3-10x)=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(x+8)-(-10x+3)=0

We multiply parentheses

2/3x-4x-(-10x+3)-32=0

We get rid of parentheses

2/3x-4x+10x-3-32=0

We multiply all the terms by the denominator


-4x*3x+10x*3x-3*3x-32*3x+2=0

Wy multiply elements

-12x^2+30x^2-9x-96x+2=0

We add all the numbers together, and all the variables

18x^2-105x+2=0

a = 18; b = -105; c = +2;
Δ = b2-4ac
Δ = -1052-4·18·2
Δ = 10881
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:

$\sqrt{\Delta}=\sqrt{10881}=\sqrt{9*1209}=\sqrt{9}*\sqrt{1209}=3\sqrt{1209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-3\sqrt{1209}}{2*18}=\frac{105-3\sqrt{1209}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+3\sqrt{1209}}{2*18}=\frac{105+3\sqrt{1209}}{36}
$