-27(2=5x)^2=7-4(2+5x)^4

Solution for -27(2=5x)^2=7-4(2+5x)^4 equation:

-27(2=5x)^2=7-4(2+5x)^4

We move all terms to the left:

-27(2-(5x)^2)=0

We multiply parentheses

135x^2-54=0

a = 135; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·135·(-54)
Δ = 29160
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:

$\sqrt{\Delta}=\sqrt{29160}=\sqrt{2916*10}=\sqrt{2916}*\sqrt{10}=54\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54\sqrt{10}}{2*135}=\frac{0-54\sqrt{10}}{270}
=-\frac{54\sqrt{10}}{270}
=-\frac{\sqrt{10}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54\sqrt{10}}{2*135}=\frac{0+54\sqrt{10}}{270}
=\frac{54\sqrt{10}}{270}
=\frac{\sqrt{10}}{5}
$