A=((70+2x)*(50+2x))-120

Solution for A=((70+2x)*(50+2x))-120 equation:

=((70+2A)(50+2A))-120

We move all terms to the left:

-(((70+2A)(50+2A))-120)=0

We add all the numbers together, and all the variables

-(((2A+70)(2A+50))-120)=0

We multiply parentheses ..

-(((+4A^2+100A+140A+3500))-120)=0


We calculate terms in parentheses: -(((+4A^2+100A+140A+3500))-120), so:

((+4A^2+100A+140A+3500))-120


We calculate terms in parentheses: +((+4A^2+100A+140A+3500)), so:

(+4A^2+100A+140A+3500)

We get rid of parentheses

4A^2+100A+140A+3500

We add all the numbers together, and all the variables

4A^2+240A+3500

Back to the equation:

+(4A^2+240A+3500)


We get rid of parentheses

4A^2+240A+3500-120

We add all the numbers together, and all the variables

4A^2+240A+3380

Back to the equation:

-(4A^2+240A+3380)


We get rid of parentheses

-4A^2-240A-3380=0

a = -4; b = -240; c = -3380;
Δ = b2-4ac
Δ = -2402-4·(-4)·(-3380)
Δ = 3520
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3520}=\sqrt{64*55}=\sqrt{64}*\sqrt{55}=8\sqrt{55}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-8\sqrt{55}}{2*-4}=\frac{240-8\sqrt{55}}{-8}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+8\sqrt{55}}{2*-4}=\frac{240+8\sqrt{55}}{-8}
$