x(1.25+0.25x)=3

Solution for x(1.25+0.25x)=3 equation:

x(1.25+0.25x)=3

We move all terms to the left:

x(1.25+0.25x)-(3)=0

We add all the numbers together, and all the variables

x(0.25x+1.25)-3=0

We multiply parentheses

0x^2+1.25x-3=0

We add all the numbers together, and all the variables

x^2+1.25x-3=0

a = 1; b = 1.25; c = -3;
Δ = b2-4ac
Δ = 1.252-4·1·(-3)
Δ = 13.5625
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{-(1.25)-\sqrt{13.5625}}{2*1}=\frac{-1.25-\sqrt{13.5625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.25)+\sqrt{13.5625}}{2*1}=\frac{-1.25+\sqrt{13.5625}}{2}
$