4a^2+52a-231=0

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

4a^2+52a-231=0

a = 4; b = 52; c = -231;
Δ = b2-4ac
Δ = 522-4·4·(-231)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-80}{2*4}=\frac{-132}{8}
=-16+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+80}{2*4}=\frac{28}{8}
=3+1/2
$