6x(x-5)=20

Solution for 6x(x-5)=20 equation:

6x(x-5)=20

We move all terms to the left:

6x(x-5)-(20)=0

We multiply parentheses

6x^2-30x-20=0

a = 6; b = -30; c = -20;
Δ = b2-4ac
Δ = -302-4·6·(-20)
Δ = 1380
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:

$\sqrt{\Delta}=\sqrt{1380}=\sqrt{4*345}=\sqrt{4}*\sqrt{345}=2\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{345}}{2*6}=\frac{30-2\sqrt{345}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{345}}{2*6}=\frac{30+2\sqrt{345}}{12}
$