6x-24=(1/2)(5+2x+7)

Solution for 6x-24=(1/2)(5+2x+7) equation:

6x-24=(1/2)(5+2x+7)

We move all terms to the left:

6x-24-((1/2)(5+2x+7))=0


Domain of the equation: 2)(5+2x+7))!=0

x∈R


We add all the numbers together, and all the variables

6x-((+1/2)(2x+12))-24=0

We multiply parentheses ..

-((+2x^2+1/2*12))+6x-24=0

We multiply all the terms by the denominator


-((+2x^2+1+6x*2*12))-24*2*12))=0


We calculate terms in parentheses: -((+2x^2+1+6x*2*12)), so:

(+2x^2+1+6x*2*12)

We get rid of parentheses

2x^2+6x*2*12+1

Wy multiply elements

2x^2+144x*1+1

Wy multiply elements

2x^2+144x+1

Back to the equation:

-(2x^2+144x+1)


We add all the numbers together, and all the variables

-(2x^2+144x+1)=0

We get rid of parentheses

-2x^2-144x-1=0

a = -2; b = -144; c = -1;
Δ = b2-4ac
Δ = -1442-4·(-2)·(-1)
Δ = 20728
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:

$\sqrt{\Delta}=\sqrt{20728}=\sqrt{4*5182}=\sqrt{4}*\sqrt{5182}=2\sqrt{5182}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-2\sqrt{5182}}{2*-2}=\frac{144-2\sqrt{5182}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+2\sqrt{5182}}{2*-2}=\frac{144+2\sqrt{5182}}{-4}
$