x^2-2,23x=5

Solution for x^2-2,23x=5 equation:

x^2-2.23x=5

We move all terms to the left:

x^2-2.23x-(5)=0

a = 1; b = -2.23; c = -5;
Δ = b2-4ac
Δ = -2.232-4·1·(-5)
Δ = 24.9729
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{-(-2.23)-\sqrt{24.9729}}{2*1}=\frac{2.23-\sqrt{24.9729}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.23)+\sqrt{24.9729}}{2*1}=\frac{2.23+\sqrt{24.9729}}{2}
$