3x^2+30x+71=0

Solution for 3x^2+30x+71=0 equation:

3x^2+30x+71=0

a = 3; b = 30; c = +71;
Δ = b2-4ac
Δ = 302-4·3·71
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-4\sqrt{3}}{2*3}=\frac{-30-4\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+4\sqrt{3}}{2*3}=\frac{-30+4\sqrt{3}}{6}
$