5x(x-8)=125

Solution for 5x(x-8)=125 equation:

5x(x-8)=125

We move all terms to the left:

5x(x-8)-(125)=0

We multiply parentheses

5x^2-40x-125=0

a = 5; b = -40; c = -125;
Δ = b2-4ac
Δ = -402-4·5·(-125)
Δ = 4100
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:

$\sqrt{\Delta}=\sqrt{4100}=\sqrt{100*41}=\sqrt{100}*\sqrt{41}=10\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{41}}{2*5}=\frac{40-10\sqrt{41}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{41}}{2*5}=\frac{40+10\sqrt{41}}{10}
$