-10^2-3a^2=-310

Solution for -10^2-3a^2=-310 equation:

-10^2-3a^2=-310

We move all terms to the left:

-10^2-3a^2-(-310)=0

We add all the numbers together, and all the variables

-3a^2+210=0

a = -3; b = 0; c = +210;
Δ = b2-4ac
Δ = 02-4·(-3)·210
Δ = 2520
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:

$\sqrt{\Delta}=\sqrt{2520}=\sqrt{36*70}=\sqrt{36}*\sqrt{70}=6\sqrt{70}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{70}}{2*-3}=\frac{0-6\sqrt{70}}{-6}
=-\frac{6\sqrt{70}}{-6}
=-\frac{\sqrt{70}}{-1}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{70}}{2*-3}=\frac{0+6\sqrt{70}}{-6}
=\frac{6\sqrt{70}}{-6}
=\frac{\sqrt{70}}{-1}
$