30a=-a^2+7000

Solution for 30a=-a^2+7000 equation:

30a=-a^2+7000

We move all terms to the left:

30a-(-a^2+7000)=0

We get rid of parentheses

a^2+30a-7000=0

a = 1; b = 30; c = -7000;
Δ = b2-4ac
Δ = 302-4·1·(-7000)
Δ = 28900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28900}=170$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-170}{2*1}=\frac{-200}{2}
=-100
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+170}{2*1}=\frac{140}{2}
=70
$