60=x(2x-7)

Solution for 60=x(2x-7) equation:

60=x(2x-7)

We move all terms to the left:

60-(x(2x-7))=0


We calculate terms in parentheses: -(x(2x-7)), so:

x(2x-7)

We multiply parentheses

2x^2-7x

Back to the equation:

-(2x^2-7x)


We get rid of parentheses

-2x^2+7x+60=0

a = -2; b = 7; c = +60;
Δ = b2-4ac
Δ = 72-4·(-2)·60
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-23}{2*-2}=\frac{-30}{-4}
=7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+23}{2*-2}=\frac{16}{-4}
=-4
$