5x^2=289

Solution for 5x^2=289 equation:

5x^2=289

We move all terms to the left:

5x^2-(289)=0

a = 5; b = 0; c = -289;
Δ = b2-4ac
Δ = 02-4·5·(-289)
Δ = 5780
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:

$\sqrt{\Delta}=\sqrt{5780}=\sqrt{1156*5}=\sqrt{1156}*\sqrt{5}=34\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-34\sqrt{5}}{2*5}=\frac{0-34\sqrt{5}}{10}
=-\frac{34\sqrt{5}}{10}
=-\frac{17\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+34\sqrt{5}}{2*5}=\frac{0+34\sqrt{5}}{10}
=\frac{34\sqrt{5}}{10}
=\frac{17\sqrt{5}}{5}
$