36x^2+84x+6=0

Solution for 36x^2+84x+6=0 equation:

36x^2+84x+6=0

a = 36; b = 84; c = +6;
Δ = b2-4ac
Δ = 842-4·36·6
Δ = 6192
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:

$\sqrt{\Delta}=\sqrt{6192}=\sqrt{144*43}=\sqrt{144}*\sqrt{43}=12\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-12\sqrt{43}}{2*36}=\frac{-84-12\sqrt{43}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+12\sqrt{43}}{2*36}=\frac{-84+12\sqrt{43}}{72}
$