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

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

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

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

-12x-(+2/3x)-30=0

We get rid of parentheses

-12x-2/3x-30=0

We multiply all the terms by the denominator


-12x*3x-30*3x-2=0

Wy multiply elements

-36x^2-90x-2=0

a = -36; b = -90; c = -2;
Δ = b2-4ac
Δ = -902-4·(-36)·(-2)
Δ = 7812
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:

$\sqrt{\Delta}=\sqrt{7812}=\sqrt{36*217}=\sqrt{36}*\sqrt{217}=6\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{217}}{2*-36}=\frac{90-6\sqrt{217}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{217}}{2*-36}=\frac{90+6\sqrt{217}}{-72}
$