5+21x2=52

Solution for 5+21x2=52 equation:

5+21x^2=52

We move all terms to the left:

5+21x^2-(52)=0

We add all the numbers together, and all the variables

21x^2-47=0

a = 21; b = 0; c = -47;
Δ = b2-4ac
Δ = 02-4·21·(-47)
Δ = 3948
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:

$\sqrt{\Delta}=\sqrt{3948}=\sqrt{4*987}=\sqrt{4}*\sqrt{987}=2\sqrt{987}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{987}}{2*21}=\frac{0-2\sqrt{987}}{42}
=-\frac{2\sqrt{987}}{42}
=-\frac{\sqrt{987}}{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{987}}{2*21}=\frac{0+2\sqrt{987}}{42}
=\frac{2\sqrt{987}}{42}
=\frac{\sqrt{987}}{21}
$