4x^2+32-1=235

Solution for 4x^2+32-1=235 equation:

4x^2+32-1=235

We move all terms to the left:

4x^2+32-1-(235)=0

We add all the numbers together, and all the variables

4x^2-204=0

a = 4; b = 0; c = -204;
Δ = b2-4ac
Δ = 02-4·4·(-204)
Δ = 3264
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:

$\sqrt{\Delta}=\sqrt{3264}=\sqrt{64*51}=\sqrt{64}*\sqrt{51}=8\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{51}}{2*4}=\frac{0-8\sqrt{51}}{8}
=-\frac{8\sqrt{51}}{8}
=-\sqrt{51}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{51}}{2*4}=\frac{0+8\sqrt{51}}{8}
=\frac{8\sqrt{51}}{8}
=\sqrt{51}
$