15x(2x-3x)=4x(x+8)

Solution for 15x(2x-3x)=4x(x+8) equation:

15x(2x-3x)=4x(x+8)

We move all terms to the left:

15x(2x-3x)-(4x(x+8))=0

We add all the numbers together, and all the variables

15x(-1x)-(4x(x+8))=0

We multiply parentheses

-15x^2-(4x(x+8))=0


We calculate terms in parentheses: -(4x(x+8)), so:

4x(x+8)

We multiply parentheses

4x^2+32x

Back to the equation:

-(4x^2+32x)


We get rid of parentheses

-15x^2-4x^2-32x=0

We add all the numbers together, and all the variables

-19x^2-32x=0

a = -19; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-19)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-19}=\frac{0}{-38}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-19}=\frac{64}{-38}
=-1+13/19
$