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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+3x^2+9x+x+3)-60=0

We get rid of parentheses

3x^2+9x+x+3-60=0

We add all the numbers together, and all the variables

3x^2+10x-57=0

a = 3; b = 10; c = -57;
Δ = b2-4ac
Δ = 102-4·3·(-57)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-28}{2*3}=\frac{-38}{6}
=-6+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+28}{2*3}=\frac{18}{6}
=3
$