-2(x-5)=6(3+1/3x)

Solution for -2(x-5)=6(3+1/3x) equation:

-2(x-5)=6(3+1/3x)

We move all terms to the left:

-2(x-5)-(6(3+1/3x))=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-2(x-5)-(6(1/3x+3))=0

We multiply parentheses

-2x-(6(1/3x+3))+10=0

We multiply all the terms by the denominator


-2x*3x+10*3x+3))-(6(1+3))=0

We add all the numbers together, and all the variables

-2x*3x+10*3x+3))-(64)=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-6x^2+30x=0

a = -6; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-6)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-6}=\frac{-60}{-12}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-6}=\frac{0}{-12}
=0
$