(X-49)(x+1)=0

Solution for (X-49)(x+1)=0 equation:

(X-49)(X+1)=0

We multiply parentheses ..

(+X^2+X-49X-49)=0

We get rid of parentheses

X^2+X-49X-49=0

We add all the numbers together, and all the variables

X^2-48X-49=0

a = 1; b = -48; c = -49;
Δ = b2-4ac
Δ = -482-4·1·(-49)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-50}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+50}{2*1}=\frac{98}{2}
=49
$