3x(x-5)=3x+8

Solution for 3x(x-5)=3x+8 equation:

3x(x-5)=3x+8

We move all terms to the left:

3x(x-5)-(3x+8)=0

We multiply parentheses

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

We get rid of parentheses

3x^2-15x-3x-8=0

We add all the numbers together, and all the variables

3x^2-18x-8=0

a = 3; b = -18; c = -8;
Δ = b2-4ac
Δ = -182-4·3·(-8)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{105}}{2*3}=\frac{18-2\sqrt{105}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{105}}{2*3}=\frac{18+2\sqrt{105}}{6}
$