5(x+8)-7x=-(2x-4)12x+21=3(4x+6)

Solution for 5(x+8)-7x=-(2x-4)12x+21=3(4x+6) equation:

5(x+8)-7x=-(2x-4)12x+21=3(4x+6)

We move all terms to the left:

5(x+8)-7x-(-(2x-4)12x+21)=0

We add all the numbers together, and all the variables

-7x+5(x+8)-(-(2x-4)12x+21)=0

We multiply parentheses

-7x+5x-(-(2x-4)12x+21)+40=0


We calculate terms in parentheses: -(-(2x-4)12x+21), so:

-(2x-4)12x+21

We multiply parentheses

-24x^2+48x+21

Back to the equation:

-(-24x^2+48x+21)


We add all the numbers together, and all the variables

-(-24x^2+48x+21)-2x+40=0

We get rid of parentheses

24x^2-48x-2x-21+40=0

We add all the numbers together, and all the variables

24x^2-50x+19=0

a = 24; b = -50; c = +19;
Δ = b2-4ac
Δ = -502-4·24·19
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-26}{2*24}=\frac{24}{48}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+26}{2*24}=\frac{76}{48}
=1+7/12
$