7(x+9)=x(x-1)

Solution for 7(x+9)=x(x-1) equation:

7(x+9)=x(x-1)

We move all terms to the left:

7(x+9)-(x(x-1))=0

We multiply parentheses

7x-(x(x-1))+63=0


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

x(x-1)

We multiply parentheses

x^2-1x

Back to the equation:

-(x^2-1x)


We get rid of parentheses

-x^2+7x+1x+63=0

We add all the numbers together, and all the variables

-1x^2+8x+63=0

a = -1; b = 8; c = +63;
Δ = b2-4ac
Δ = 82-4·(-1)·63
Δ = 316
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{79}}{2*-1}=\frac{-8-2\sqrt{79}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{79}}{2*-1}=\frac{-8+2\sqrt{79}}{-2}
$