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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -((5x+8)3x), so:

(5x+8)3x

We multiply parentheses

15x^2+24x

Back to the equation:

-(15x^2+24x)


We get rid of parentheses

-15x^2+x-24x=0

We add all the numbers together, and all the variables

-15x^2-23x=0

a = -15; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-15)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-15}=\frac{46}{-30}
=-1+8/15
$