x=(5x+15)(3x-3)

Solution for x=(5x+15)(3x-3) equation:

x=(5x+15)(3x-3)

We move all terms to the left:

x-((5x+15)(3x-3))=0

We multiply parentheses ..

-((+15x^2-15x+45x-45))+x=0


We calculate terms in parentheses: -((+15x^2-15x+45x-45)), so:

(+15x^2-15x+45x-45)

We get rid of parentheses

15x^2-15x+45x-45

We add all the numbers together, and all the variables

15x^2+30x-45

Back to the equation:

-(15x^2+30x-45)


We add all the numbers together, and all the variables

x-(15x^2+30x-45)=0

We get rid of parentheses

-15x^2+x-30x+45=0

We add all the numbers together, and all the variables

-15x^2-29x+45=0

a = -15; b = -29; c = +45;
Δ = b2-4ac
Δ = -292-4·(-15)·45
Δ = 3541
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-\sqrt{3541}}{2*-15}=\frac{29-\sqrt{3541}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{3541}}{2*-15}=\frac{29+\sqrt{3541}}{-30}
$