4a^2-40a=-84

Solution for 4a^2-40a=-84 equation:

4a^2-40a=-84

We move all terms to the left:

4a^2-40a-(-84)=0

We add all the numbers together, and all the variables

4a^2-40a+84=0

a = 4; b = -40; c = +84;
Δ = b2-4ac
Δ = -402-4·4·84
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-16}{2*4}=\frac{24}{8}
=3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+16}{2*4}=\frac{56}{8}
=7
$