4x^2+3x+1=231

Solution for 4x^2+3x+1=231 equation:

4x^2+3x+1=231

We move all terms to the left:

4x^2+3x+1-(231)=0

We add all the numbers together, and all the variables

4x^2+3x-230=0

a = 4; b = 3; c = -230;
Δ = b2-4ac
Δ = 32-4·4·(-230)
Δ = 3689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{3689}}{2*4}=\frac{-3-\sqrt{3689}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{3689}}{2*4}=\frac{-3+\sqrt{3689}}{8}
$