0=x^2+16x-152

Solution for 0=x^2+16x-152 equation:

0=x^2+16x-152

We move all terms to the left:

0-(x^2+16x-152)=0

We add all the numbers together, and all the variables

-(x^2+16x-152)=0

We get rid of parentheses

-x^2-16x+152=0

We add all the numbers together, and all the variables

-1x^2-16x+152=0

a = -1; b = -16; c = +152;
Δ = b2-4ac
Δ = -162-4·(-1)·152
Δ = 864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12\sqrt{6}}{2*-1}=\frac{16-12\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12\sqrt{6}}{2*-1}=\frac{16+12\sqrt{6}}{-2}
$