0=a^2+10a-156

Solution for 0=a^2+10a-156 equation:

0=a^2+10a-156

We move all terms to the left:

0-(a^2+10a-156)=0

We add all the numbers together, and all the variables

-(a^2+10a-156)=0

We get rid of parentheses

-a^2-10a+156=0

We add all the numbers together, and all the variables

-1a^2-10a+156=0

a = -1; b = -10; c = +156;
Δ = b2-4ac
Δ = -102-4·(-1)·156
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{181}}{2*-1}=\frac{10-2\sqrt{181}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{181}}{2*-1}=\frac{10+2\sqrt{181}}{-2}
$