60^2=(x+6)(3x-6)

Solution for 60^2=(x+6)(3x-6) equation:

60^2=(x+6)(3x-6)

We move all terms to the left:

60^2-((x+6)(3x-6))=0

We add all the numbers together, and all the variables

-((x+6)(3x-6))+3600=0

We multiply parentheses ..

-((+3x^2-6x+18x-36))+3600=0


We calculate terms in parentheses: -((+3x^2-6x+18x-36)), so:

(+3x^2-6x+18x-36)

We get rid of parentheses

3x^2-6x+18x-36

We add all the numbers together, and all the variables

3x^2+12x-36

Back to the equation:

-(3x^2+12x-36)


We get rid of parentheses

-3x^2-12x+36+3600=0

We add all the numbers together, and all the variables

-3x^2-12x+3636=0

a = -3; b = -12; c = +3636;
Δ = b2-4ac
Δ = -122-4·(-3)·3636
Δ = 43776
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:

$\sqrt{\Delta}=\sqrt{43776}=\sqrt{2304*19}=\sqrt{2304}*\sqrt{19}=48\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-48\sqrt{19}}{2*-3}=\frac{12-48\sqrt{19}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+48\sqrt{19}}{2*-3}=\frac{12+48\sqrt{19}}{-6}
$