x^2+48x=-245

Solution for x^2+48x=-245 equation:

x^2+48x=-245

We move all terms to the left:

x^2+48x-(-245)=0

We add all the numbers together, and all the variables

x^2+48x+245=0

a = 1; b = 48; c = +245;
Δ = b2-4ac
Δ = 482-4·1·245
Δ = 1324
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:

$\sqrt{\Delta}=\sqrt{1324}=\sqrt{4*331}=\sqrt{4}*\sqrt{331}=2\sqrt{331}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{331}}{2*1}=\frac{-48-2\sqrt{331}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{331}}{2*1}=\frac{-48+2\sqrt{331}}{2}
$