3(x-13)(x-3)=5

Solution for 3(x-13)(x-3)=5 equation:

3(x-13)(x-3)=5

We move all terms to the left:

3(x-13)(x-3)-(5)=0

We multiply parentheses ..

3(+x^2-3x-13x+39)-5=0

We multiply parentheses

3x^2-9x-39x+117-5=0

We add all the numbers together, and all the variables

3x^2-48x+112=0

a = 3; b = -48; c = +112;
Δ = b2-4ac
Δ = -482-4·3·112
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{15}}{2*3}=\frac{48-8\sqrt{15}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{15}}{2*3}=\frac{48+8\sqrt{15}}{6}
$