4x^2-7=205

Solution for 4x^2-7=205 equation:

4x^2-7=205

We move all terms to the left:

4x^2-7-(205)=0

We add all the numbers together, and all the variables

4x^2-212=0

a = 4; b = 0; c = -212;
Δ = b2-4ac
Δ = 02-4·4·(-212)
Δ = 3392
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:

$\sqrt{\Delta}=\sqrt{3392}=\sqrt{64*53}=\sqrt{64}*\sqrt{53}=8\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{53}}{2*4}=\frac{0-8\sqrt{53}}{8}
=-\frac{8\sqrt{53}}{8}
=-\sqrt{53}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{53}}{2*4}=\frac{0+8\sqrt{53}}{8}
=\frac{8\sqrt{53}}{8}
=\sqrt{53}
$