x2-3x+0,5=25

Solution for x2-3x+0,5=25 equation:

x2-3x+0.5=25

We move all terms to the left:

x2-3x+0.5-(25)=0

We add all the numbers together, and all the variables

x^2-3x-24.5=0

a = 1; b = -3; c = -24.5;
Δ = b2-4ac
Δ = -32-4·1·(-24.5)
Δ = 107
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{-(-3)-\sqrt{107}}{2*1}=\frac{3-\sqrt{107}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{107}}{2*1}=\frac{3+\sqrt{107}}{2}
$