49x^2-29=0

Solution for 49x^2-29=0 equation:

49x^2-29=0

a = 49; b = 0; c = -29;
Δ = b2-4ac
Δ = 02-4·49·(-29)
Δ = 5684
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:

$\sqrt{\Delta}=\sqrt{5684}=\sqrt{196*29}=\sqrt{196}*\sqrt{29}=14\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{29}}{2*49}=\frac{0-14\sqrt{29}}{98}
=-\frac{14\sqrt{29}}{98}
=-\frac{\sqrt{29}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{29}}{2*49}=\frac{0+14\sqrt{29}}{98}
=\frac{14\sqrt{29}}{98}
=\frac{\sqrt{29}}{7}
$