66^2=x(x+5)

Solution for 66^2=x(x+5) equation:

66^2=x(x+5)

We move all terms to the left:

66^2-(x(x+5))=0

We add all the numbers together, and all the variables

-(x(x+5))+4356=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 get rid of parentheses

-x^2-5x+4356=0

We add all the numbers together, and all the variables

-1x^2-5x+4356=0

a = -1; b = -5; c = +4356;
Δ = b2-4ac
Δ = -52-4·(-1)·4356
Δ = 17449
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{-(-5)-\sqrt{17449}}{2*-1}=\frac{5-\sqrt{17449}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{17449}}{2*-1}=\frac{5+\sqrt{17449}}{-2}
$