0=x^2-4x-240

Solution for 0=x^2-4x-240 equation:

0=x^2-4x-240

We move all terms to the left:

0-(x^2-4x-240)=0

We add all the numbers together, and all the variables

-(x^2-4x-240)=0

We get rid of parentheses

-x^2+4x+240=0

We add all the numbers together, and all the variables

-1x^2+4x+240=0

a = -1; b = 4; c = +240;
Δ = b2-4ac
Δ = 42-4·(-1)·240
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{61}}{2*-1}=\frac{-4-4\sqrt{61}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{61}}{2*-1}=\frac{-4+4\sqrt{61}}{-2}
$