10x(x-5)=80

Solution for 10x(x-5)=80 equation:

10x(x-5)=80

We move all terms to the left:

10x(x-5)-(80)=0

We multiply parentheses

10x^2-50x-80=0

a = 10; b = -50; c = -80;
Δ = b2-4ac
Δ = -502-4·10·(-80)
Δ = 5700
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:

$\sqrt{\Delta}=\sqrt{5700}=\sqrt{100*57}=\sqrt{100}*\sqrt{57}=10\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{57}}{2*10}=\frac{50-10\sqrt{57}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{57}}{2*10}=\frac{50+10\sqrt{57}}{20}
$