6x(x-8)-29=0

Solution for 6x(x-8)-29=0 equation:

6x(x-8)-29=0

We multiply parentheses

6x^2-48x-29=0

a = 6; b = -48; c = -29;
Δ = b2-4ac
Δ = -482-4·6·(-29)
Δ = 3000
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:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-10\sqrt{30}}{2*6}=\frac{48-10\sqrt{30}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+10\sqrt{30}}{2*6}=\frac{48+10\sqrt{30}}{12}
$