4x(3x+8)-9=2(6x-8)+39

Solution for 4x(3x+8)-9=2(6x-8)+39 equation:

4x(3x+8)-9=2(6x-8)+39

We move all terms to the left:

4x(3x+8)-9-(2(6x-8)+39)=0

We multiply parentheses

12x^2+32x-(2(6x-8)+39)-9=0


We calculate terms in parentheses: -(2(6x-8)+39), so:

2(6x-8)+39

We multiply parentheses

12x-16+39

We add all the numbers together, and all the variables

12x+23

Back to the equation:

-(12x+23)


We get rid of parentheses

12x^2+32x-12x-23-9=0

We add all the numbers together, and all the variables

12x^2+20x-32=0

a = 12; b = 20; c = -32;
Δ = b2-4ac
Δ = 202-4·12·(-32)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-44}{2*12}=\frac{-64}{24}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+44}{2*12}=\frac{24}{24}
=1
$