58x^2-100=0

Solution for 58x^2-100=0 equation:

58x^2-100=0

a = 58; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·58·(-100)
Δ = 23200
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:

$\sqrt{\Delta}=\sqrt{23200}=\sqrt{400*58}=\sqrt{400}*\sqrt{58}=20\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{58}}{2*58}=\frac{0-20\sqrt{58}}{116}
=-\frac{20\sqrt{58}}{116}
=-\frac{5\sqrt{58}}{29}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{58}}{2*58}=\frac{0+20\sqrt{58}}{116}
=\frac{20\sqrt{58}}{116}
=\frac{5\sqrt{58}}{29}
$