-10a-3a^2=-310

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

-10a-3a^2=-310

We move all terms to the left:

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

We add all the numbers together, and all the variables

-3a^2-10a+310=0

a = -3; b = -10; c = +310;
Δ = b2-4ac
Δ = -102-4·(-3)·310
Δ = 3820
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:

$\sqrt{\Delta}=\sqrt{3820}=\sqrt{4*955}=\sqrt{4}*\sqrt{955}=2\sqrt{955}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{955}}{2*-3}=\frac{10-2\sqrt{955}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{955}}{2*-3}=\frac{10+2\sqrt{955}}{-6}
$