8(x-10)x=20

Solution for 8(x-10)x=20 equation:

8(x-10)x=20

We move all terms to the left:

8(x-10)x-(20)=0

We multiply parentheses

8x^2-80x-20=0

a = 8; b = -80; c = -20;
Δ = b2-4ac
Δ = -802-4·8·(-20)
Δ = 7040
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:

$\sqrt{\Delta}=\sqrt{7040}=\sqrt{64*110}=\sqrt{64}*\sqrt{110}=8\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{110}}{2*8}=\frac{80-8\sqrt{110}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{110}}{2*8}=\frac{80+8\sqrt{110}}{16}
$