(6x-42)(x+28)=60

Solution for (6x-42)(x+28)=60 equation:

(6x-42)(x+28)=60

We move all terms to the left:

(6x-42)(x+28)-(60)=0

We multiply parentheses ..

(+6x^2+168x-42x-1176)-60=0

We get rid of parentheses

6x^2+168x-42x-1176-60=0

We add all the numbers together, and all the variables

6x^2+126x-1236=0

a = 6; b = 126; c = -1236;
Δ = b2-4ac
Δ = 1262-4·6·(-1236)
Δ = 45540
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:

$\sqrt{\Delta}=\sqrt{45540}=\sqrt{36*1265}=\sqrt{36}*\sqrt{1265}=6\sqrt{1265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-6\sqrt{1265}}{2*6}=\frac{-126-6\sqrt{1265}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+6\sqrt{1265}}{2*6}=\frac{-126+6\sqrt{1265}}{12}
$