x(2x-7)=60

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

x(2x-7)=60

We move all terms to the left:

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

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