(9*(x*x)+63*x)/2=441

Solution for (9*(x*x)+63*x)/2=441 equation:

(9*(x*x)+63*x)/2=441

We move all terms to the left:

(9*(x*x)+63*x)/2-(441)=0

We add all the numbers together, and all the variables

(9*(+x*x)+63*x)/2-441=0

We multiply all the terms by the denominator


(9*(+x*x)+63*x)-441*2=0


We calculate terms in parentheses: +(9*(+x*x)+63*x), so:

9*(+x*x)+63*x

We add all the numbers together, and all the variables

63x+9*(+x*x)

We multiply parentheses

9x^2+63x

Back to the equation:

+(9x^2+63x)


We add all the numbers together, and all the variables

(9x^2+63x)-882=0

We get rid of parentheses

9x^2+63x-882=0

a = 9; b = 63; c = -882;
Δ = b2-4ac
Δ = 632-4·9·(-882)
Δ = 35721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{35721}=189$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-189}{2*9}=\frac{-252}{18}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+189}{2*9}=\frac{126}{18}
=7
$