(2x-61)(6x)=3

Solution for (2x-61)(6x)=3 equation:

(2x-61)(6x)=3

We move all terms to the left:

(2x-61)(6x)-(3)=0

We multiply parentheses

12x^2-366x-3=0

a = 12; b = -366; c = -3;
Δ = b2-4ac
Δ = -3662-4·12·(-3)
Δ = 134100
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:

$\sqrt{\Delta}=\sqrt{134100}=\sqrt{900*149}=\sqrt{900}*\sqrt{149}=30\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-366)-30\sqrt{149}}{2*12}=\frac{366-30\sqrt{149}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-366)+30\sqrt{149}}{2*12}=\frac{366+30\sqrt{149}}{24}
$