x^2+100-29x^2=0

Solution for x^2+100-29x^2=0 equation:

x^2+100-29x^2=0

We add all the numbers together, and all the variables

-28x^2+100=0

a = -28; b = 0; c = +100;
Δ = b2-4ac
Δ = 02-4·(-28)·100
Δ = 11200
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:

$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{7}}{2*-28}=\frac{0-40\sqrt{7}}{-56}
=-\frac{40\sqrt{7}}{-56}
=-\frac{5\sqrt{7}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{7}}{2*-28}=\frac{0+40\sqrt{7}}{-56}
=\frac{40\sqrt{7}}{-56}
=\frac{5\sqrt{7}}{-7}
$