A=x^2+51x

Solution for A=x^2+51x equation:

=A^2+51A

We move all terms to the left:

-(A^2+51A)=0

We get rid of parentheses

-A^2-51A=0

We add all the numbers together, and all the variables

-1A^2-51A=0

a = -1; b = -51; c = 0;
Δ = b2-4ac
Δ = -512-4·(-1)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-51}{2*-1}=\frac{0}{-2}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+51}{2*-1}=\frac{102}{-2}
=-51
$