A=-5x2+78x+21

Solution for A=-5x2+78x+21 equation:

=-5A^2+78A+21

We move all terms to the left:

-(-5A^2+78A+21)=0

We get rid of parentheses

5A^2-78A-21=0

a = 5; b = -78; c = -21;
Δ = b2-4ac
Δ = -782-4·5·(-21)
Δ = 6504
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:

$\sqrt{\Delta}=\sqrt{6504}=\sqrt{4*1626}=\sqrt{4}*\sqrt{1626}=2\sqrt{1626}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1626}}{2*5}=\frac{78-2\sqrt{1626}}{10}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1626}}{2*5}=\frac{78+2\sqrt{1626}}{10}
$