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

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+3A^2+21A-8A-56))=0


We calculate terms in parentheses: -((+3A^2+21A-8A-56)), so:

(+3A^2+21A-8A-56)

We get rid of parentheses

3A^2+21A-8A-56

We add all the numbers together, and all the variables

3A^2+13A-56

Back to the equation:

-(3A^2+13A-56)


We get rid of parentheses

-3A^2-13A+56=0

a = -3; b = -13; c = +56;
Δ = b2-4ac
Δ = -132-4·(-3)·56
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-29}{2*-3}=\frac{-16}{-6}
=2+2/3
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+29}{2*-3}=\frac{42}{-6}
=-7
$