.5(2x+4)+8=(6x-3)(2/3)

Solution for .5(2x+4)+8=(6x-3)(2/3) equation:

.5(2x+4)+8=(6x-3)(2/3)

We move all terms to the left:

.5(2x+4)+8-((6x-3)(2/3))=0

We add all the numbers together, and all the variables

.5(2x+4)-((6x-3)(+2/3))+8=0

We multiply parentheses

x-((6x-3)(+2/3))+2+8=0

We multiply parentheses ..

-((+12x^2-3*2/3))+x+2+8=0

We multiply all the terms by the denominator


-((+12x^2-3*2+x*3))+2*3))+8*3))=0


We calculate terms in parentheses: -((+12x^2-3*2+x*3)), so:

(+12x^2-3*2+x*3)

We get rid of parentheses

12x^2+x*3-3*2

We add all the numbers together, and all the variables

12x^2+x*3-6

Wy multiply elements

12x^2+3x-6

Back to the equation:

-(12x^2+3x-6)


We add all the numbers together, and all the variables

-(12x^2+3x-6)=0

We get rid of parentheses

-12x^2-3x+6=0

a = -12; b = -3; c = +6;
Δ = b2-4ac
Δ = -32-4·(-12)·6
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{33}}{2*-12}=\frac{3-3\sqrt{33}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{33}}{2*-12}=\frac{3+3\sqrt{33}}{-24}
$