0=x^2+8x-148

Solution for 0=x^2+8x-148 equation:

0=x^2+8x-148

We move all terms to the left:

0-(x^2+8x-148)=0

We add all the numbers together, and all the variables

-(x^2+8x-148)=0

We get rid of parentheses

-x^2-8x+148=0

We add all the numbers together, and all the variables

-1x^2-8x+148=0

a = -1; b = -8; c = +148;
Δ = b2-4ac
Δ = -82-4·(-1)·148
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{41}}{2*-1}=\frac{8-4\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{41}}{2*-1}=\frac{8+4\sqrt{41}}{-2}
$