A=(4x+7)(8x+2)

Solution for A=(4x+7)(8x+2) equation:

=(4A+7)(8A+2)

We move all terms to the left:

-((4A+7)(8A+2))=0

We multiply parentheses ..

-((+32A^2+8A+56A+14))=0


We calculate terms in parentheses: -((+32A^2+8A+56A+14)), so:

(+32A^2+8A+56A+14)

We get rid of parentheses

32A^2+8A+56A+14

We add all the numbers together, and all the variables

32A^2+64A+14

Back to the equation:

-(32A^2+64A+14)


We get rid of parentheses

-32A^2-64A-14=0

a = -32; b = -64; c = -14;
Δ = b2-4ac
Δ = -642-4·(-32)·(-14)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-48}{2*-32}=\frac{16}{-64}
=-1/4
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+48}{2*-32}=\frac{112}{-64}
=-1+3/4
$