A=2x^2+4x-21

Solution for A=2x^2+4x-21 equation:

=2A^2+4A-21

We move all terms to the left:

-(2A^2+4A-21)=0

We get rid of parentheses

-2A^2-4A+21=0

a = -2; b = -4; c = +21;
Δ = b2-4ac
Δ = -42-4·(-2)·21
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{46}}{2*-2}=\frac{4-2\sqrt{46}}{-4}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{46}}{2*-2}=\frac{4+2\sqrt{46}}{-4}
$