3x(x-1)=5x+8

Solution for 3x(x-1)=5x+8 equation:

3x(x-1)=5x+8

We move all terms to the left:

3x(x-1)-(5x+8)=0

We multiply parentheses

3x^2-3x-(5x+8)=0

We get rid of parentheses

3x^2-3x-5x-8=0

We add all the numbers together, and all the variables

3x^2-8x-8=0

a = 3; b = -8; c = -8;
Δ = b2-4ac
Δ = -82-4·3·(-8)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{10}}{2*3}=\frac{8-4\sqrt{10}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{10}}{2*3}=\frac{8+4\sqrt{10}}{6}
$