3x-15+7x=5xx(x-9)

Solution for 3x-15+7x=5xx(x-9) equation:

3x-15+7x=5xx(x-9)

We move all terms to the left:

3x-15+7x-(5xx(x-9))=0

We add all the numbers together, and all the variables

10x-(5xx(x-9))-15=0


We calculate terms in parentheses: -(5xx(x-9)), so:

5xx(x-9)

We multiply parentheses

5x^2-45x

Back to the equation:

-(5x^2-45x)


We get rid of parentheses

-5x^2+10x+45x-15=0

We add all the numbers together, and all the variables

-5x^2+55x-15=0

a = -5; b = 55; c = -15;
Δ = b2-4ac
Δ = 552-4·(-5)·(-15)
Δ = 2725
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:

$\sqrt{\Delta}=\sqrt{2725}=\sqrt{25*109}=\sqrt{25}*\sqrt{109}=5\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-5\sqrt{109}}{2*-5}=\frac{-55-5\sqrt{109}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+5\sqrt{109}}{2*-5}=\frac{-55+5\sqrt{109}}{-10}
$