x(0.25x+0.5)=1

Solution for x(0.25x+0.5)=1 equation:

x(0.25x+0.5)=1

We move all terms to the left:

x(0.25x+0.5)-(1)=0

We multiply parentheses

0x^2+0.5x-1=0

We add all the numbers together, and all the variables

x^2+0.5x-1=0

a = 1; b = 0.5; c = -1;
Δ = b2-4ac
Δ = 0.52-4·1·(-1)
Δ = 4.25
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{-(0.5)-\sqrt{4.25}}{2*1}=\frac{-0.5-\sqrt{4.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{4.25}}{2*1}=\frac{-0.5+\sqrt{4.25}}{2}
$