0=-0.054x^2+1.43x-8

Solution for 0=-0.054x^2+1.43x-8 equation:

0=-0.054x^2+1.43x-8

We move all terms to the left:

0-(-0.054x^2+1.43x-8)=0

We add all the numbers together, and all the variables

-(-0.054x^2+1.43x-8)=0

We get rid of parentheses

0.054x^2-1.43x+8=0

a = 0.054; b = -1.43; c = +8;
Δ = b2-4ac
Δ = -1.432-4·0.054·8
Δ = 0.3169
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{-(-1.43)-\sqrt{0.3169}}{2*0.054}=\frac{1.43-\sqrt{0.3169}}{0.108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.43)+\sqrt{0.3169}}{2*0.054}=\frac{1.43+\sqrt{0.3169}}{0.108}
$