x(x-10)=144

Solution for x(x-10)=144 equation:

x(x-10)=144

We move all terms to the left:

x(x-10)-(144)=0

We multiply parentheses

x^2-10x-144=0

a = 1; b = -10; c = -144;
Δ = b2-4ac
Δ = -102-4·1·(-144)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-26}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+26}{2*1}=\frac{36}{2}
=18
$