3x(x-3)=8

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

3x(x-3)=8

We move all terms to the left:

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

We multiply parentheses

3x^2-9x-8=0

a = 3; b = -9; c = -8;
Δ = b2-4ac
Δ = -92-4·3·(-8)
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{177}}{2*3}=\frac{9-\sqrt{177}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{177}}{2*3}=\frac{9+\sqrt{177}}{6}
$