2x(x-3)=0.25

Solution for 2x(x-3)=0.25 equation:

2x(x-3)=0.25

We move all terms to the left:

2x(x-3)-(0.25)=0

We add all the numbers together, and all the variables

2x(x-3)-0.25=0

We multiply parentheses

2x^2-6x-0.25=0

a = 2; b = -6; c = -0.25;
Δ = b2-4ac
Δ = -62-4·2·(-0.25)
Δ = 38
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-\sqrt{38}}{2*2}=\frac{6-\sqrt{38}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+\sqrt{38}}{2*2}=\frac{6+\sqrt{38}}{4}
$