36x^2-24x-38=0

Solution for 36x^2-24x-38=0 equation:

36x^2-24x-38=0

a = 36; b = -24; c = -38;
Δ = b2-4ac
Δ = -242-4·36·(-38)
Δ = 6048
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:

$\sqrt{\Delta}=\sqrt{6048}=\sqrt{144*42}=\sqrt{144}*\sqrt{42}=12\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{42}}{2*36}=\frac{24-12\sqrt{42}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{42}}{2*36}=\frac{24+12\sqrt{42}}{72}
$