x^2=25x-144

Solution for x^2=25x-144 equation:

x^2=25x-144

We move all terms to the left:

x^2-(25x-144)=0

We get rid of parentheses

x^2-25x+144=0

a = 1; b = -25; c = +144;
Δ = b2-4ac
Δ = -252-4·1·144
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-7}{2*1}=\frac{18}{2}
=9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+7}{2*1}=\frac{32}{2}
=16
$