-6x^2+22x+45=0

Solution for -6x^2+22x+45=0 equation:

-6x^2+22x+45=0

a = -6; b = 22; c = +45;
Δ = b2-4ac
Δ = 222-4·(-6)·45
Δ = 1564
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:

$\sqrt{\Delta}=\sqrt{1564}=\sqrt{4*391}=\sqrt{4}*\sqrt{391}=2\sqrt{391}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{391}}{2*-6}=\frac{-22-2\sqrt{391}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{391}}{2*-6}=\frac{-22+2\sqrt{391}}{-12}
$