47(47)=x(x+41)

Solution for 47(47)=x(x+41) equation:

47(47)=x(x+41)

We move all terms to the left:

47(47)-(x(x+41))=0


We calculate terms in parentheses: -(x(x+41)), so:

x(x+41)

We multiply parentheses

x^2+41x

Back to the equation:

-(x^2+41x)


We get rid of parentheses

-x^2-41x+4747=0

We add all the numbers together, and all the variables

-1x^2-41x+4747=0

a = -1; b = -41; c = +4747;
Δ = b2-4ac
Δ = -412-4·(-1)·4747
Δ = 20669
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{-(-41)-\sqrt{20669}}{2*-1}=\frac{41-\sqrt{20669}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{20669}}{2*-1}=\frac{41+\sqrt{20669}}{-2}
$