-9x^2-6x+224=0

Solution for -9x^2-6x+224=0 equation:

-9x^2-6x+224=0

a = -9; b = -6; c = +224;
Δ = b2-4ac
Δ = -62-4·(-9)·224
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-90}{2*-9}=\frac{-84}{-18}
=4+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+90}{2*-9}=\frac{96}{-18}
=-5+1/3
$