3(x+8)=2(2x+16)x=

Solution for 3(x+8)=2(2x+16)x= equation:

3(x+8)=2(2x+16)x=

We move all terms to the left:

3(x+8)-(2(2x+16)x)=0

We multiply parentheses

3x-(2(2x+16)x)+24=0


We calculate terms in parentheses: -(2(2x+16)x), so:

2(2x+16)x

We multiply parentheses

4x^2+32x

Back to the equation:

-(4x^2+32x)


We get rid of parentheses

-4x^2+3x-32x+24=0

We add all the numbers together, and all the variables

-4x^2-29x+24=0

a = -4; b = -29; c = +24;
Δ = b2-4ac
Δ = -292-4·(-4)·24
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-35}{2*-4}=\frac{-6}{-8}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+35}{2*-4}=\frac{64}{-8}
=-8
$