4a^2+52-231=0

Solution for 4a^2+52-231=0 equation:

4a^2+52-231=0

We add all the numbers together, and all the variables

4a^2-179=0

a = 4; b = 0; c = -179;
Δ = b2-4ac
Δ = 02-4·4·(-179)
Δ = 2864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2864}=\sqrt{16*179}=\sqrt{16}*\sqrt{179}=4\sqrt{179}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{179}}{2*4}=\frac{0-4\sqrt{179}}{8}
=-\frac{4\sqrt{179}}{8}
=-\frac{\sqrt{179}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{179}}{2*4}=\frac{0+4\sqrt{179}}{8}
=\frac{4\sqrt{179}}{8}
=\frac{\sqrt{179}}{2}
$