6x^2+84x+20=0

Solution for 6x^2+84x+20=0 equation:

6x^2+84x+20=0

a = 6; b = 84; c = +20;
Δ = b2-4ac
Δ = 842-4·6·20
Δ = 6576
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:

$\sqrt{\Delta}=\sqrt{6576}=\sqrt{16*411}=\sqrt{16}*\sqrt{411}=4\sqrt{411}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{411}}{2*6}=\frac{-84-4\sqrt{411}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{411}}{2*6}=\frac{-84+4\sqrt{411}}{12}
$