5x^2+30x+31=0

Solution for 5x^2+30x+31=0 equation:

5x^2+30x+31=0

a = 5; b = 30; c = +31;
Δ = b2-4ac
Δ = 302-4·5·31
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{70}}{2*5}=\frac{-30-2\sqrt{70}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{70}}{2*5}=\frac{-30+2\sqrt{70}}{10}
$