15x+(13x-9)=9x(7x-9)-13

Solution for 15x+(13x-9)=9x(7x-9)-13 equation:

15x+(13x-9)=9x(7x-9)-13

We move all terms to the left:

15x+(13x-9)-(9x(7x-9)-13)=0

We get rid of parentheses

15x+13x-(9x(7x-9)-13)-9=0


We calculate terms in parentheses: -(9x(7x-9)-13), so:

9x(7x-9)-13

We multiply parentheses

63x^2-81x-13

Back to the equation:

-(63x^2-81x-13)


We add all the numbers together, and all the variables

28x-(63x^2-81x-13)-9=0

We get rid of parentheses

-63x^2+28x+81x+13-9=0

We add all the numbers together, and all the variables

-63x^2+109x+4=0

a = -63; b = 109; c = +4;
Δ = b2-4ac
Δ = 1092-4·(-63)·4
Δ = 12889
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{-(109)-\sqrt{12889}}{2*-63}=\frac{-109-\sqrt{12889}}{-126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(109)+\sqrt{12889}}{2*-63}=\frac{-109+\sqrt{12889}}{-126}
$