0.75x^2+0.25X=0.25

Solution for 0.75x^2+0.25X=0.25 equation:

0.75x^2+0.25x=0.25

We move all terms to the left:

0.75x^2+0.25x-(0.25)=0

We add all the numbers together, and all the variables

0.75x^2+0.25x-0.25=0

a = 0.75; b = 0.25; c = -0.25;
Δ = b2-4ac
Δ = 0.252-4·0.75·(-0.25)
Δ = 0.8125
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{-(0.25)-\sqrt{0.8125}}{2*0.75}=\frac{-0.25-\sqrt{0.8125}}{1.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.25)+\sqrt{0.8125}}{2*0.75}=\frac{-0.25+\sqrt{0.8125}}{1.5}
$