x(x+42)=138

Solution for x(x+42)=138 equation:

x(x+42)=138

We move all terms to the left:

x(x+42)-(138)=0

We multiply parentheses

x^2+42x-138=0

a = 1; b = 42; c = -138;
Δ = b2-4ac
Δ = 422-4·1·(-138)
Δ = 2316
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2316}=\sqrt{4*579}=\sqrt{4}*\sqrt{579}=2\sqrt{579}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{579}}{2*1}=\frac{-42-2\sqrt{579}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{579}}{2*1}=\frac{-42+2\sqrt{579}}{2}
$