27x^2+36x-37=0

Solution for 27x^2+36x-37=0 equation:

27x^2+36x-37=0

a = 27; b = 36; c = -37;
Δ = b2-4ac
Δ = 362-4·27·(-37)
Δ = 5292
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:

$\sqrt{\Delta}=\sqrt{5292}=\sqrt{1764*3}=\sqrt{1764}*\sqrt{3}=42\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-42\sqrt{3}}{2*27}=\frac{-36-42\sqrt{3}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+42\sqrt{3}}{2*27}=\frac{-36+42\sqrt{3}}{54}
$