21x2-100=5

Solution for 21x2-100=5 equation:

21x^2-100=5

We move all terms to the left:

21x^2-100-(5)=0

We add all the numbers together, and all the variables

21x^2-105=0

a = 21; b = 0; c = -105;
Δ = b2-4ac
Δ = 02-4·21·(-105)
Δ = 8820
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:

$\sqrt{\Delta}=\sqrt{8820}=\sqrt{1764*5}=\sqrt{1764}*\sqrt{5}=42\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42\sqrt{5}}{2*21}=\frac{0-42\sqrt{5}}{42}
=-\frac{42\sqrt{5}}{42}
=-\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42\sqrt{5}}{2*21}=\frac{0+42\sqrt{5}}{42}
=\frac{42\sqrt{5}}{42}
=\sqrt{5}
$