70a=-a^2+6000

Solution for 70a=-a^2+6000 equation:

70a=-a^2+6000

We move all terms to the left:

70a-(-a^2+6000)=0

We get rid of parentheses

a^2+70a-6000=0

a = 1; b = 70; c = -6000;
Δ = b2-4ac
Δ = 702-4·1·(-6000)
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{-(70)-170}{2*1}=\frac{-240}{2}
=-120
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+170}{2*1}=\frac{100}{2}
=50
$