5x^2+1=471

Solution for 5x^2+1=471 equation:

5x^2+1=471

We move all terms to the left:

5x^2+1-(471)=0

We add all the numbers together, and all the variables

5x^2-470=0

a = 5; b = 0; c = -470;
Δ = b2-4ac
Δ = 02-4·5·(-470)
Δ = 9400
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:

$\sqrt{\Delta}=\sqrt{9400}=\sqrt{100*94}=\sqrt{100}*\sqrt{94}=10\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{94}}{2*5}=\frac{0-10\sqrt{94}}{10}
=-\frac{10\sqrt{94}}{10}
=-\sqrt{94}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{94}}{2*5}=\frac{0+10\sqrt{94}}{10}
=\frac{10\sqrt{94}}{10}
=\sqrt{94}
$