x^2-2.5x=1=0

Solution for x^2-2.5x=1=0 equation:

x^2-2.5x=1=0

We move all terms to the left:

x^2-2.5x-(1)=0

a = 1; b = -2.5; c = -1;
Δ = b2-4ac
Δ = -2.52-4·1·(-1)
Δ = 10.25
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{-(-2.5)-\sqrt{10.25}}{2*1}=\frac{2.5-\sqrt{10.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{10.25}}{2*1}=\frac{2.5+\sqrt{10.25}}{2}
$