(13x+9)=(7x+7)(5x+11)

Solution for (13x+9)=(7x+7)(5x+11) equation:

(13x+9)=(7x+7)(5x+11)

We move all terms to the left:

(13x+9)-((7x+7)(5x+11))=0

We get rid of parentheses

13x-((7x+7)(5x+11))+9=0

We multiply parentheses ..

-((+35x^2+77x+35x+77))+13x+9=0


We calculate terms in parentheses: -((+35x^2+77x+35x+77)), so:

(+35x^2+77x+35x+77)

We get rid of parentheses

35x^2+77x+35x+77

We add all the numbers together, and all the variables

35x^2+112x+77

Back to the equation:

-(35x^2+112x+77)


We add all the numbers together, and all the variables

13x-(35x^2+112x+77)+9=0

We get rid of parentheses

-35x^2+13x-112x-77+9=0

We add all the numbers together, and all the variables

-35x^2-99x-68=0

a = -35; b = -99; c = -68;
Δ = b2-4ac
Δ = -992-4·(-35)·(-68)
Δ = 281
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{-(-99)-\sqrt{281}}{2*-35}=\frac{99-\sqrt{281}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+\sqrt{281}}{2*-35}=\frac{99+\sqrt{281}}{-70}
$