5x(3x-2)=8

Solution for 5x(3x-2)=8 equation:

5x(3x-2)=8

We move all terms to the left:

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

We multiply parentheses

15x^2-10x-8=0

a = 15; b = -10; c = -8;
Δ = b2-4ac
Δ = -102-4·15·(-8)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{145}}{2*15}=\frac{10-2\sqrt{145}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{145}}{2*15}=\frac{10+2\sqrt{145}}{30}
$