25x^2-89=0

Solution for 25x^2-89=0 equation:

25x^2-89=0

a = 25; b = 0; c = -89;
Δ = b2-4ac
Δ = 02-4·25·(-89)
Δ = 8900
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:

$\sqrt{\Delta}=\sqrt{8900}=\sqrt{100*89}=\sqrt{100}*\sqrt{89}=10\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{89}}{2*25}=\frac{0-10\sqrt{89}}{50}
=-\frac{10\sqrt{89}}{50}
=-\frac{\sqrt{89}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{89}}{2*25}=\frac{0+10\sqrt{89}}{50}
=\frac{10\sqrt{89}}{50}
=\frac{\sqrt{89}}{5}
$