X*x+0.25x-3.5=0

Solution for X*x+0.25x-3.5=0 equation:

X*X+0.25X-3.5=0

We add all the numbers together, and all the variables

0.25X+X*X-3.5=0

Wy multiply elements

X^2+0.25X-3.5=0

a = 1; b = 0.25; c = -3.5;
Δ = b2-4ac
Δ = 0.252-4·1·(-3.5)
Δ = 14.0625
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{14.0625}}{2*1}=\frac{-0.25-\sqrt{14.0625}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.25)+\sqrt{14.0625}}{2*1}=\frac{-0.25+\sqrt{14.0625}}{2}
$