5x(-x-11)=5x-7x(-x-7)

Solution for 5x(-x-11)=5x-7x(-x-7) equation:

5x(-x-11)=5x-7x(-x-7)

We move all terms to the left:

5x(-x-11)-(5x-7x(-x-7))=0

We add all the numbers together, and all the variables

5x(-1x-11)-(5x-7x(-1x-7))=0

We multiply parentheses

-5x^2-55x-(5x-7x(-1x-7))=0


We calculate terms in parentheses: -(5x-7x(-1x-7)), so:

5x-7x(-1x-7)

We multiply parentheses

7x^2+5x+49x

We add all the numbers together, and all the variables

7x^2+54x

Back to the equation:

-(7x^2+54x)


We get rid of parentheses

-5x^2-7x^2-55x-54x=0

We add all the numbers together, and all the variables

-12x^2-109x=0

a = -12; b = -109; c = 0;
Δ = b2-4ac
Δ = -1092-4·(-12)·0
Δ = 11881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11881}=109$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109)-109}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109)+109}{2*-12}=\frac{218}{-24}
=-9+1/12
$