A=(4x-7)(3+8x)

Solution for A=(4x-7)(3+8x) equation:

=(4A-7)(3+8A)

We move all terms to the left:

-((4A-7)(3+8A))=0

We add all the numbers together, and all the variables

-((4A-7)(8A+3))=0

We multiply parentheses ..

-((+32A^2+12A-56A-21))=0


We calculate terms in parentheses: -((+32A^2+12A-56A-21)), so:

(+32A^2+12A-56A-21)

We get rid of parentheses

32A^2+12A-56A-21

We add all the numbers together, and all the variables

32A^2-44A-21

Back to the equation:

-(32A^2-44A-21)


We get rid of parentheses

-32A^2+44A+21=0

a = -32; b = 44; c = +21;
Δ = b2-4ac
Δ = 442-4·(-32)·21
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-68}{2*-32}=\frac{-112}{-64}
=1+3/4
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+68}{2*-32}=\frac{24}{-64}
=-3/8
$