x(10+x)=144

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

x(10+x)=144

We move all terms to the left:

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

We add all the numbers together, and all the variables

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