.5328(a^2+69a+4761)=5000

Solution for .5328(a^2+69a+4761)=5000 equation:

.5328(a^2+69a+4761)=5000

We move all terms to the left:

.5328(a^2+69a+4761)-(5000)=0

We multiply parentheses

0.5328a^2+36.7632a+2536.6608-5000=0

We add all the numbers together, and all the variables

0.5328a^2+36.7632a-2463.3392=0

a = 0.5328; b = 36.7632; c = -2463.3392;
Δ = b2-4ac
Δ = 36.76322-4·0.5328·(-2463.3392)
Δ = 6601.40137728
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36.7632)-\sqrt{6601.40137728}}{2*0.5328}=\frac{-36.7632-\sqrt{6601.40137728}}{1.0656}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36.7632)+\sqrt{6601.40137728}}{2*0.5328}=\frac{-36.7632+\sqrt{6601.40137728}}{1.0656}
$