7x=x(x-6)

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

7x=x(x-6)

We move all terms to the left:

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


We calculate terms in parentheses: -(x(x-6)), so:

x(x-6)

We multiply parentheses

x^2-6x

Back to the equation:

-(x^2-6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+13x=0

a = -1; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-1)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-1}=\frac{-26}{-2}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-1}=\frac{0}{-2}
=0
$