4x^2+1=235

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

4x^2+1=235

We move all terms to the left:

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

We add all the numbers together, and all the variables

4x^2-234=0

a = 4; b = 0; c = -234;
Δ = b2-4ac
Δ = 02-4·4·(-234)
Δ = 3744
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:

$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{26}}{2*4}=\frac{0-12\sqrt{26}}{8}
=-\frac{12\sqrt{26}}{8}
=-\frac{3\sqrt{26}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{26}}{2*4}=\frac{0+12\sqrt{26}}{8}
=\frac{12\sqrt{26}}{8}
=\frac{3\sqrt{26}}{2}
$