2x(3x+8)=5x-8x

Solution for 2x(3x+8)=5x-8x equation:

2x(3x+8)=5x-8x

We move all terms to the left:

2x(3x+8)-(5x-8x)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

6x^2+16x-(-3x)=0

We get rid of parentheses

6x^2+16x+3x=0

We add all the numbers together, and all the variables

6x^2+19x=0

a = 6; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·6·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*6}=\frac{-38}{12}
=-3+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*6}=\frac{0}{12}
=0
$