(-3x^2)+22x-8=0

Solution for (-3x^2)+22x-8=0 equation:

(-3x^2)+22x-8=0

We get rid of parentheses

-3x^2+22x-8=0

a = -3; b = 22; c = -8;
Δ = b2-4ac
Δ = 222-4·(-3)·(-8)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{97}}{2*-3}=\frac{-22-2\sqrt{97}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{97}}{2*-3}=\frac{-22+2\sqrt{97}}{-6}
$