5x2+1=106

Solution for 5x2+1=106 equation:

5x^2+1=106

We move all terms to the left:

5x^2+1-(106)=0

We add all the numbers together, and all the variables

5x^2-105=0

a = 5; b = 0; c = -105;
Δ = b2-4ac
Δ = 02-4·5·(-105)
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{21}}{2*5}=\frac{0-10\sqrt{21}}{10}
=-\frac{10\sqrt{21}}{10}
=-\sqrt{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{21}}{2*5}=\frac{0+10\sqrt{21}}{10}
=\frac{10\sqrt{21}}{10}
=\sqrt{21}
$