65=x*(x+4)

Solution for 65=x*(x+4) equation:

65=x(x+4)

We move all terms to the left:

65-(x(x+4))=0


We calculate terms in parentheses: -(x(x+4)), so:

x(x+4)

We multiply parentheses

x^2+4x

Back to the equation:

-(x^2+4x)


We get rid of parentheses

-x^2-4x+65=0

We add all the numbers together, and all the variables

-1x^2-4x+65=0

a = -1; b = -4; c = +65;
Δ = b2-4ac
Δ = -42-4·(-1)·65
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{69}}{2*-1}=\frac{4-2\sqrt{69}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{69}}{2*-1}=\frac{4+2\sqrt{69}}{-2}
$