X2+4=29,x2-4

Solution for X2+4=29,x2-4 equation:

X2+4=29.X^2-4

We move all terms to the left:

X2+4-(29.X^2-4)=0

We add all the numbers together, and all the variables

X^2-(29.X^2-4)+4=0

We get rid of parentheses

X^2-29.X^2+4+4=0

We add all the numbers together, and all the variables

-28X^2+8=0

a = -28; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-28)·8
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*-28}=\frac{0-8\sqrt{14}}{-56}
=-\frac{8\sqrt{14}}{-56}
=-\frac{\sqrt{14}}{-7}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*-28}=\frac{0+8\sqrt{14}}{-56}
=\frac{8\sqrt{14}}{-56}
=\frac{\sqrt{14}}{-7}
$