x-7(6+x-7)=x(5+x)

Solution for x-7(6+x-7)=x(5+x) equation:

x-7(6+x-7)=x(5+x)

We move all terms to the left:

x-7(6+x-7)-(x(5+x))=0

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

x(x+5)

We multiply parentheses

x^2+5x

Back to the equation:

-(x^2+5x)


We add all the numbers together, and all the variables

-6x-(x^2+5x)+7=0

We get rid of parentheses

-x^2-6x-5x+7=0

We add all the numbers together, and all the variables

-1x^2-11x+7=0

a = -1; b = -11; c = +7;
Δ = b2-4ac
Δ = -112-4·(-1)·7
Δ = 149
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{-(-11)-\sqrt{149}}{2*-1}=\frac{11-\sqrt{149}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{149}}{2*-1}=\frac{11+\sqrt{149}}{-2}
$