3x(x-8)=29

Solution for 3x(x-8)=29 equation:

3x(x-8)=29

We move all terms to the left:

3x(x-8)-(29)=0

We multiply parentheses

3x^2-24x-29=0

a = 3; b = -24; c = -29;
Δ = b2-4ac
Δ = -242-4·3·(-29)
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{231}}{2*3}=\frac{24-2\sqrt{231}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{231}}{2*3}=\frac{24+2\sqrt{231}}{6}
$