0=6x^2-42x-60

Solution for 0=6x^2-42x-60 equation:

0=6x^2-42x-60

We move all terms to the left:

0-(6x^2-42x-60)=0

We add all the numbers together, and all the variables

-(6x^2-42x-60)=0

We get rid of parentheses

-6x^2+42x+60=0

a = -6; b = 42; c = +60;
Δ = b2-4ac
Δ = 422-4·(-6)·60
Δ = 3204
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:

$\sqrt{\Delta}=\sqrt{3204}=\sqrt{36*89}=\sqrt{36}*\sqrt{89}=6\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{89}}{2*-6}=\frac{-42-6\sqrt{89}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{89}}{2*-6}=\frac{-42+6\sqrt{89}}{-12}
$