0=5x^2-55.66x+154.9

Solution for 0=5x^2-55.66x+154.9 equation:

0=5x^2-55.66x+154.9

We move all terms to the left:

0-(5x^2-55.66x+154.9)=0

We add all the numbers together, and all the variables

-(5x^2-55.66x+154.9)=0

We get rid of parentheses

-5x^2+55.66x-154.9=0

a = -5; b = 55.66; c = -154.9;
Δ = b2-4ac
Δ = 55.662-4·(-5)·(-154.9)
Δ = 0.0355999999997
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{-(55.66)-\sqrt{0.0355999999997}}{2*-5}=\frac{-55.66-\sqrt{0.0355999999997}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55.66)+\sqrt{0.0355999999997}}{2*-5}=\frac{-55.66+\sqrt{0.0355999999997}}{-10}
$