x(21+x)=(x+1)(22+14)

Solution for x(21+x)=(x+1)(22+14) equation:

x(21+x)=(x+1)(22+14)

We move all terms to the left:

x(21+x)-((x+1)(22+14))=0

We add all the numbers together, and all the variables

x(x+21)-((x+1)36)=0

We multiply parentheses

x^2+21x-((x+1)36)=0


We calculate terms in parentheses: -((x+1)36), so:

(x+1)36

We multiply parentheses

36x+36

Back to the equation:

-(36x+36)


We get rid of parentheses

x^2+21x-36x-36=0

We add all the numbers together, and all the variables

x^2-15x-36=0

a = 1; b = -15; c = -36;
Δ = b2-4ac
Δ = -152-4·1·(-36)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{41}}{2*1}=\frac{15-3\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{41}}{2*1}=\frac{15+3\sqrt{41}}{2}
$