A(x)=7(x^2+14x)-56

Solution for A(x)=7(x^2+14x)-56 equation:

(A)=7(A^2+14A)-56

We move all terms to the left:

(A)-(7(A^2+14A)-56)=0


We calculate terms in parentheses: -(7(A^2+14A)-56), so:

7(A^2+14A)-56

We multiply parentheses

7A^2+98A-56

Back to the equation:

-(7A^2+98A-56)


We get rid of parentheses

-7A^2+A-98A+56=0

We add all the numbers together, and all the variables

-7A^2-97A+56=0

a = -7; b = -97; c = +56;
Δ = b2-4ac
Δ = -972-4·(-7)·56
Δ = 10977
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-97)-\sqrt{10977}}{2*-7}=\frac{97-\sqrt{10977}}{-14}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-97)+\sqrt{10977}}{2*-7}=\frac{97+\sqrt{10977}}{-14}
$