x2-4.6x+5.29=62

Solution for x2-4.6x+5.29=62 equation:

x2-4.6x+5.29=62

We move all terms to the left:

x2-4.6x+5.29-(62)=0

We add all the numbers together, and all the variables

x^2-4.6x-56.71=0

a = 1; b = -4.6; c = -56.71;
Δ = b2-4ac
Δ = -4.62-4·1·(-56.71)
Δ = 248
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{248}=\sqrt{4*62}=\sqrt{4}*\sqrt{62}=2\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4.6)-2\sqrt{62}}{2*1}=\frac{4.6-2\sqrt{62}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.6)+2\sqrt{62}}{2*1}=\frac{4.6+2\sqrt{62}}{2}
$