36x^2+96x+1=0

Solution for 36x^2+96x+1=0 equation:

36x^2+96x+1=0

a = 36; b = 96; c = +1;
Δ = b2-4ac
Δ = 962-4·36·1
Δ = 9072
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:

$\sqrt{\Delta}=\sqrt{9072}=\sqrt{1296*7}=\sqrt{1296}*\sqrt{7}=36\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-36\sqrt{7}}{2*36}=\frac{-96-36\sqrt{7}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+36\sqrt{7}}{2*36}=\frac{-96+36\sqrt{7}}{72}
$