x^2+3x+.25=0

Solution for x^2+3x+.25=0 equation:

x^2+3x+.25=0

We add all the numbers together, and all the variables

x^2+3x+0.25=0

a = 1; b = 3; c = +0.25;
Δ = b2-4ac
Δ = 32-4·1·0.25
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-2\sqrt{2}}{2*1}=\frac{-3-2\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+2\sqrt{2}}{2*1}=\frac{-3+2\sqrt{2}}{2}
$