A=(x+4)(2x-23)

Solution for A=(x+4)(2x-23) equation:

=(A+4)(2A-23)

We move all terms to the left:

-((A+4)(2A-23))=0

We multiply parentheses ..

-((+2A^2-23A+8A-92))=0


We calculate terms in parentheses: -((+2A^2-23A+8A-92)), so:

(+2A^2-23A+8A-92)

We get rid of parentheses

2A^2-23A+8A-92

We add all the numbers together, and all the variables

2A^2-15A-92

Back to the equation:

-(2A^2-15A-92)


We get rid of parentheses

-2A^2+15A+92=0

a = -2; b = 15; c = +92;
Δ = b2-4ac
Δ = 152-4·(-2)·92
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-31}{2*-2}=\frac{-46}{-4}
=11+1/2
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+31}{2*-2}=\frac{16}{-4}
=-4
$