3x+13=(9x-15)(2x-8)

Solution for 3x+13=(9x-15)(2x-8) equation:

3x+13=(9x-15)(2x-8)

We move all terms to the left:

3x+13-((9x-15)(2x-8))=0

We multiply parentheses ..

-((+18x^2-72x-30x+120))+3x+13=0


We calculate terms in parentheses: -((+18x^2-72x-30x+120)), so:

(+18x^2-72x-30x+120)

We get rid of parentheses

18x^2-72x-30x+120

We add all the numbers together, and all the variables

18x^2-102x+120

Back to the equation:

-(18x^2-102x+120)


We add all the numbers together, and all the variables

3x-(18x^2-102x+120)+13=0

We get rid of parentheses

-18x^2+3x+102x-120+13=0

We add all the numbers together, and all the variables

-18x^2+105x-107=0

a = -18; b = 105; c = -107;
Δ = b2-4ac
Δ = 1052-4·(-18)·(-107)
Δ = 3321
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:

$\sqrt{\Delta}=\sqrt{3321}=\sqrt{81*41}=\sqrt{81}*\sqrt{41}=9\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-9\sqrt{41}}{2*-18}=\frac{-105-9\sqrt{41}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+9\sqrt{41}}{2*-18}=\frac{-105+9\sqrt{41}}{-36}
$