5x(3+x)=60

Solution for 5x(3+x)=60 equation:

5x(3+x)=60

We move all terms to the left:

5x(3+x)-(60)=0

We add all the numbers together, and all the variables

5x(x+3)-60=0

We multiply parentheses

5x^2+15x-60=0

a = 5; b = 15; c = -60;
Δ = b2-4ac
Δ = 152-4·5·(-60)
Δ = 1425
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:

$\sqrt{\Delta}=\sqrt{1425}=\sqrt{25*57}=\sqrt{25}*\sqrt{57}=5\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{57}}{2*5}=\frac{-15-5\sqrt{57}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{57}}{2*5}=\frac{-15+5\sqrt{57}}{10}
$