60=2x(3x+5)

Solution for 60=2x(3x+5) equation:

60=2x(3x+5)

We move all terms to the left:

60-(2x(3x+5))=0


We calculate terms in parentheses: -(2x(3x+5)), so:

2x(3x+5)

We multiply parentheses

6x^2+10x

Back to the equation:

-(6x^2+10x)


We get rid of parentheses

-6x^2-10x+60=0

a = -6; b = -10; c = +60;
Δ = b2-4ac
Δ = -102-4·(-6)·60
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{385}}{2*-6}=\frac{10-2\sqrt{385}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{385}}{2*-6}=\frac{10+2\sqrt{385}}{-12}
$