x(3x+5)=138

Solution for x(3x+5)=138 equation:

x(3x+5)=138

We move all terms to the left:

x(3x+5)-(138)=0

We multiply parentheses

3x^2+5x-138=0

a = 3; b = 5; c = -138;
Δ = b2-4ac
Δ = 52-4·3·(-138)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-41}{2*3}=\frac{-46}{6}
=-7+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+41}{2*3}=\frac{36}{6}
=6
$