21x^2-126+29=0

Solution for 21x^2-126+29=0 equation:

21x^2-126+29=0

We add all the numbers together, and all the variables

21x^2-97=0

a = 21; b = 0; c = -97;
Δ = b2-4ac
Δ = 02-4·21·(-97)
Δ = 8148
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:

$\sqrt{\Delta}=\sqrt{8148}=\sqrt{4*2037}=\sqrt{4}*\sqrt{2037}=2\sqrt{2037}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2037}}{2*21}=\frac{0-2\sqrt{2037}}{42}
=-\frac{2\sqrt{2037}}{42}
=-\frac{\sqrt{2037}}{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2037}}{2*21}=\frac{0+2\sqrt{2037}}{42}
=\frac{2\sqrt{2037}}{42}
=\frac{\sqrt{2037}}{21}
$