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

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

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

We move all terms to the left:

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

We multiply parentheses

9x-((x-5)(x-3))-45=0

We multiply parentheses ..

-((+x^2-3x-5x+15))+9x-45=0


We calculate terms in parentheses: -((+x^2-3x-5x+15)), so:

(+x^2-3x-5x+15)

We get rid of parentheses

x^2-3x-5x+15

We add all the numbers together, and all the variables

x^2-8x+15

Back to the equation:

-(x^2-8x+15)


We add all the numbers together, and all the variables

9x-(x^2-8x+15)-45=0

We get rid of parentheses

-x^2+9x+8x-15-45=0

We add all the numbers together, and all the variables

-1x^2+17x-60=0

a = -1; b = 17; c = -60;
Δ = b2-4ac
Δ = 172-4·(-1)·(-60)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-7}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+7}{2*-1}=\frac{-10}{-2}
=+5
$