2x^2-24x-60=3

Solution for 2x^2-24x-60=3 equation:

2x^2-24x-60=3

We move all terms to the left:

2x^2-24x-60-(3)=0

We add all the numbers together, and all the variables

2x^2-24x-63=0

a = 2; b = -24; c = -63;
Δ = b2-4ac
Δ = -242-4·2·(-63)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{30}}{2*2}=\frac{24-6\sqrt{30}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{30}}{2*2}=\frac{24+6\sqrt{30}}{4}
$