x^2+23=19x-25

Solution for x^2+23=19x-25 equation:

x^2+23=19x-25

We move all terms to the left:

x^2+23-(19x-25)=0

We get rid of parentheses

x^2-19x+25+23=0

We add all the numbers together, and all the variables

x^2-19x+48=0

a = 1; b = -19; c = +48;
Δ = b2-4ac
Δ = -192-4·1·48
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-13}{2*1}=\frac{6}{2}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+13}{2*1}=\frac{32}{2}
=16
$