x^2-10x-0.5=150

Solution for x^2-10x-0.5=150 equation:

x^2-10x-0.5=150

We move all terms to the left:

x^2-10x-0.5-(150)=0

We add all the numbers together, and all the variables

x^2-10x-150.5=0

a = 1; b = -10; c = -150.5;
Δ = b2-4ac
Δ = -102-4·1·(-150.5)
Δ = 702
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:

$\sqrt{\Delta}=\sqrt{702}=\sqrt{9*78}=\sqrt{9}*\sqrt{78}=3\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-3\sqrt{78}}{2*1}=\frac{10-3\sqrt{78}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+3\sqrt{78}}{2*1}=\frac{10+3\sqrt{78}}{2}
$