x^2-24x+19=-25

Solution for x^2-24x+19=-25 equation:

x^2-24x+19=-25

We move all terms to the left:

x^2-24x+19-(-25)=0

We add all the numbers together, and all the variables

x^2-24x+44=0

a = 1; b = -24; c = +44;
Δ = b2-4ac
Δ = -242-4·1·44
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-20}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+20}{2*1}=\frac{44}{2}
=22
$