-9x^2-4x+6=0

Solution for -9x^2-4x+6=0 equation:

-9x^2-4x+6=0

a = -9; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-9)·6
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{58}}{2*-9}=\frac{4-2\sqrt{58}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{58}}{2*-9}=\frac{4+2\sqrt{58}}{-18}
$