4^4-5x^2+7=0

Solution for 4^4-5x^2+7=0 equation:

4^4-5x^2+7=0

We add all the numbers together, and all the variables

-5x^2+263=0

a = -5; b = 0; c = +263;
Δ = b2-4ac
Δ = 02-4·(-5)·263
Δ = 5260
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:

$\sqrt{\Delta}=\sqrt{5260}=\sqrt{4*1315}=\sqrt{4}*\sqrt{1315}=2\sqrt{1315}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1315}}{2*-5}=\frac{0-2\sqrt{1315}}{-10}
=-\frac{2\sqrt{1315}}{-10}
=-\frac{\sqrt{1315}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1315}}{2*-5}=\frac{0+2\sqrt{1315}}{-10}
=\frac{2\sqrt{1315}}{-10}
=\frac{\sqrt{1315}}{-5}
$