-3(-8-x)=(1/3)(x+56)

Solution for -3(-8-x)=(1/3)(x+56) equation:

-3(-8-x)=(1/3)(x+56)

We move all terms to the left:

-3(-8-x)-((1/3)(x+56))=0


Domain of the equation: 3)(x+56))!=0

x∈R


We add all the numbers together, and all the variables

-3(-1x-8)-((+1/3)(x+56))=0

We multiply parentheses

3x-((+1/3)(x+56))+24=0

We multiply parentheses ..

-((+x^2+1/3*56))+3x+24=0

We multiply all the terms by the denominator


-((+x^2+1+3x*3*56))+24*3*56))=0


We calculate terms in parentheses: -((+x^2+1+3x*3*56)), so:

(+x^2+1+3x*3*56)

We get rid of parentheses

x^2+3x*3*56+1

Wy multiply elements

x^2+504x*5+1

Wy multiply elements

x^2+2520x+1

Back to the equation:

-(x^2+2520x+1)


We add all the numbers together, and all the variables

-(x^2+2520x+1)=0

We get rid of parentheses

-x^2-2520x-1=0

We add all the numbers together, and all the variables

-1x^2-2520x-1=0

a = -1; b = -2520; c = -1;
Δ = b2-4ac
Δ = -25202-4·(-1)·(-1)
Δ = 6350396
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:

$\sqrt{\Delta}=\sqrt{6350396}=\sqrt{4*1587599}=\sqrt{4}*\sqrt{1587599}=2\sqrt{1587599}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2520)-2\sqrt{1587599}}{2*-1}=\frac{2520-2\sqrt{1587599}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2520)+2\sqrt{1587599}}{2*-1}=\frac{2520+2\sqrt{1587599}}{-2}
$