138=(3x+5)x

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

138=(3x+5)x

We move all terms to the left:

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


We calculate terms in parentheses: -((3x+5)x), so:

(3x+5)x

We multiply parentheses

3x^2+5x

Back to the equation:

-(3x^2+5x)


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