5x=15x(6x+6)

Solution for 5x=15x(6x+6) equation:

5x=15x(6x+6)

We move all terms to the left:

5x-(15x(6x+6))=0


We calculate terms in parentheses: -(15x(6x+6)), so:

15x(6x+6)

We multiply parentheses

90x^2+90x

Back to the equation:

-(90x^2+90x)


We get rid of parentheses

-90x^2+5x-90x=0

We add all the numbers together, and all the variables

-90x^2-85x=0

a = -90; b = -85; c = 0;
Δ = b2-4ac
Δ = -852-4·(-90)·0
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-85}{2*-90}=\frac{0}{-180}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+85}{2*-90}=\frac{170}{-180}
=-17/18
$