x(2x-5)=125

Solution for x(2x-5)=125 equation:

x(2x-5)=125

We move all terms to the left:

x(2x-5)-(125)=0

We multiply parentheses

2x^2-5x-125=0

a = 2; b = -5; c = -125;
Δ = b2-4ac
Δ = -52-4·2·(-125)
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{41}}{2*2}=\frac{5-5\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{41}}{2*2}=\frac{5+5\sqrt{41}}{4}
$