X^2-4.25x-1=0

Solution for X^2-4.25x-1=0 equation:

X^2-4.25X-1=0

a = 1; b = -4.25; c = -1;
Δ = b2-4ac
Δ = -4.252-4·1·(-1)
Δ = 22.0625
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{-(-4.25)-\sqrt{22.0625}}{2*1}=\frac{4.25-\sqrt{22.0625}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.25)+\sqrt{22.0625}}{2*1}=\frac{4.25+\sqrt{22.0625}}{2}
$