46=5x^2

Solution for 46=5x^2 equation:

46=5x^2

We move all terms to the left:

46-(5x^2)=0

a = -5; b = 0; c = +46;
Δ = b2-4ac
Δ = 02-4·(-5)·46
Δ = 920
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:

$\sqrt{\Delta}=\sqrt{920}=\sqrt{4*230}=\sqrt{4}*\sqrt{230}=2\sqrt{230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{230}}{2*-5}=\frac{0-2\sqrt{230}}{-10}
=-\frac{2\sqrt{230}}{-10}
=-\frac{\sqrt{230}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{230}}{2*-5}=\frac{0+2\sqrt{230}}{-10}
=\frac{2\sqrt{230}}{-10}
=\frac{\sqrt{230}}{-5}
$