A=2x^2+24x+46

Solution for A=2x^2+24x+46 equation:

=2A^2+24A+46

We move all terms to the left:

-(2A^2+24A+46)=0

We get rid of parentheses

-2A^2-24A-46=0

a = -2; b = -24; c = -46;
Δ = b2-4ac
Δ = -242-4·(-2)·(-46)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{13}}{2*-2}=\frac{24-4\sqrt{13}}{-4}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{13}}{2*-2}=\frac{24+4\sqrt{13}}{-4}
$