x^2+31x+4=0

Solution for x^2+31x+4=0 equation:

x^2+31x+4=0

a = 1; b = 31; c = +4;
Δ = b2-4ac
Δ = 312-4·1·4
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-3\sqrt{105}}{2*1}=\frac{-31-3\sqrt{105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+3\sqrt{105}}{2*1}=\frac{-31+3\sqrt{105}}{2}
$