(3x+1)(2x)=60

Solution for (3x+1)(2x)=60 equation:

(3x+1)(2x)=60

We move all terms to the left:

(3x+1)(2x)-(60)=0

We multiply parentheses

6x^2+2x-60=0

a = 6; b = 2; c = -60;
Δ = b2-4ac
Δ = 22-4·6·(-60)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-38}{2*6}=\frac{-40}{12}
=-3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+38}{2*6}=\frac{36}{12}
=3
$