3(3x-3)+2x(x-5)=5(x-5)(x-3)

Solution for 3(3x-3)+2x(x-5)=5(x-5)(x-3) equation:

3(3x-3)+2x(x-5)=5(x-5)(x-3)

We move all terms to the left:

3(3x-3)+2x(x-5)-(5(x-5)(x-3))=0

We multiply parentheses

2x^2+9x-10x-(5(x-5)(x-3))-9=0

We multiply parentheses ..

2x^2-(5(+x^2-3x-5x+15))+9x-10x-9=0


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

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

We multiply parentheses

5x^2-15x-25x+75

We add all the numbers together, and all the variables

5x^2-40x+75

Back to the equation:

-(5x^2-40x+75)


We add all the numbers together, and all the variables

2x^2-1x-(5x^2-40x+75)-9=0

We get rid of parentheses

2x^2-5x^2-1x+40x-75-9=0

We add all the numbers together, and all the variables

-3x^2+39x-84=0

a = -3; b = 39; c = -84;
Δ = b2-4ac
Δ = 392-4·(-3)·(-84)
Δ = 513
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{57}}{2*-3}=\frac{-39-3\sqrt{57}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{57}}{2*-3}=\frac{-39+3\sqrt{57}}{-6}
$