-0.01x^2+0.8x=14.6

Solution for -0.01x^2+0.8x=14.6 equation:

-0.01x^2+0.8x=14.6

We move all terms to the left:

-0.01x^2+0.8x-(14.6)=0

We add all the numbers together, and all the variables

-0.01x^2+0.8x-14.6=0

a = -0.01; b = 0.8; c = -14.6;
Δ = b2-4ac
Δ = 0.82-4·(-0.01)·(-14.6)
Δ = 0.056
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{-(0.8)-\sqrt{0.056}}{2*-0.01}=\frac{-0.8-\sqrt{0.056}}{-0.02}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.8)+\sqrt{0.056}}{2*-0.01}=\frac{-0.8+\sqrt{0.056}}{-0.02}
$