6x(2x-8)+3=15

Solution for 6x(2x-8)+3=15 equation:

6x(2x-8)+3=15

We move all terms to the left:

6x(2x-8)+3-(15)=0

We add all the numbers together, and all the variables

6x(2x-8)-12=0

We multiply parentheses

12x^2-48x-12=0

a = 12; b = -48; c = -12;
Δ = b2-4ac
Δ = -482-4·12·(-12)
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24\sqrt{5}}{2*12}=\frac{48-24\sqrt{5}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24\sqrt{5}}{2*12}=\frac{48+24\sqrt{5}}{24}
$