60=5x(3x-1)

Solution for 60=5x(3x-1) equation:

60=5x(3x-1)

We move all terms to the left:

60-(5x(3x-1))=0


We calculate terms in parentheses: -(5x(3x-1)), so:

5x(3x-1)

We multiply parentheses

15x^2-5x

Back to the equation:

-(15x^2-5x)


We get rid of parentheses

-15x^2+5x+60=0

a = -15; b = 5; c = +60;
Δ = b2-4ac
Δ = 52-4·(-15)·60
Δ = 3625
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:

$\sqrt{\Delta}=\sqrt{3625}=\sqrt{25*145}=\sqrt{25}*\sqrt{145}=5\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{145}}{2*-15}=\frac{-5-5\sqrt{145}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{145}}{2*-15}=\frac{-5+5\sqrt{145}}{-30}
$