-9x^2+22x-4=0

Solution for -9x^2+22x-4=0 equation:

-9x^2+22x-4=0

a = -9; b = 22; c = -4;
Δ = b2-4ac
Δ = 222-4·(-9)·(-4)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{85}}{2*-9}=\frac{-22-2\sqrt{85}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{85}}{2*-9}=\frac{-22+2\sqrt{85}}{-18}
$