x^2+48x=100

Solution for x^2+48x=100 equation:

x^2+48x=100

We move all terms to the left:

x^2+48x-(100)=0

a = 1; b = 48; c = -100;
Δ = b2-4ac
Δ = 482-4·1·(-100)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-52}{2*1}=\frac{-100}{2}
=-50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+52}{2*1}=\frac{4}{2}
=2
$