6(5x-5)(5x-1)=0

Solution for 6(5x-5)(5x-1)=0 equation:

6(5x-5)(5x-1)=0

We multiply parentheses ..

6(+25x^2-5x-25x+5)=0

We multiply parentheses

150x^2-30x-150x+30=0

We add all the numbers together, and all the variables

150x^2-180x+30=0

a = 150; b = -180; c = +30;
Δ = b2-4ac
Δ = -1802-4·150·30
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-120}{2*150}=\frac{60}{300}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+120}{2*150}=\frac{300}{300}
=1
$