5x(3x-2)=5

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

5x(3x-2)=5

We move all terms to the left:

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

We multiply parentheses

15x^2-10x-5=0

a = 15; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·15·(-5)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20}{2*15}=\frac{-10}{30}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20}{2*15}=\frac{30}{30}
=1
$