x(2x-4)=25

Solution for x(2x-4)=25 equation:

x(2x-4)=25

We move all terms to the left:

x(2x-4)-(25)=0

We multiply parentheses

2x^2-4x-25=0

a = 2; b = -4; c = -25;
Δ = b2-4ac
Δ = -42-4·2·(-25)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6\sqrt{6}}{2*2}=\frac{4-6\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6\sqrt{6}}{2*2}=\frac{4+6\sqrt{6}}{4}
$