3(2x-7)(2x-7)=18

Solution for 3(2x-7)(2x-7)=18 equation:

3(2x-7)(2x-7)=18

We move all terms to the left:

3(2x-7)(2x-7)-(18)=0

We multiply parentheses ..

3(+4x^2-14x-14x+49)-18=0

We multiply parentheses

12x^2-42x-42x+147-18=0

We add all the numbers together, and all the variables

12x^2-84x+129=0

a = 12; b = -84; c = +129;
Δ = b2-4ac
Δ = -842-4·12·129
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-12\sqrt{6}}{2*12}=\frac{84-12\sqrt{6}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+12\sqrt{6}}{2*12}=\frac{84+12\sqrt{6}}{24}
$