-.67x^2+.83x+.83=0

Solution for -.67x^2+.83x+.83=0 equation:

-.67x^2+.83x+.83=0

We add all the numbers together, and all the variables

-0.67x^2+.83x+0.83=0

a = -0.67; b = .83; c = +0.83;
Δ = b2-4ac
Δ = .832-4·(-0.67)·0.83
Δ = 2.9133
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(.83)-\sqrt{2.9133}}{2*-0.67}=\frac{-0.83-\sqrt{2.9133}}{-1.34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(.83)+\sqrt{2.9133}}{2*-0.67}=\frac{-0.83+\sqrt{2.9133}}{-1.34}
$