A(x)=(2x+5.5)(2x+8.5)-46.75

Solution for A(x)=(2x+5.5)(2x+8.5)-46.75 equation:

(A)=(2A+5.5)(2A+8.5)-46.75

We move all terms to the left:

(A)-((2A+5.5)(2A+8.5)-46.75)=0

We multiply parentheses ..

-((+4A^2+17A+11A+46.75)-46.75)+A=0


We calculate terms in parentheses: -((+4A^2+17A+11A+46.75)-46.75), so:

(+4A^2+17A+11A+46.75)-46.75

We get rid of parentheses

4A^2+17A+11A+46.75-46.75

We add all the numbers together, and all the variables

4A^2+28A

Back to the equation:

-(4A^2+28A)


We add all the numbers together, and all the variables

A-(4A^2+28A)=0

We get rid of parentheses

-4A^2+A-28A=0

We add all the numbers together, and all the variables

-4A^2-27A=0

a = -4; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-4)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-4}=\frac{0}{-8}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-4}=\frac{54}{-8}
=-6+3/4
$