10=-5x^2+18x+1

Solution for 10=-5x^2+18x+1 equation:

10=-5x^2+18x+1

We move all terms to the left:

10-(-5x^2+18x+1)=0

We get rid of parentheses

5x^2-18x-1+10=0

We add all the numbers together, and all the variables

5x^2-18x+9=0

a = 5; b = -18; c = +9;
Δ = b2-4ac
Δ = -182-4·5·9
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12}{2*5}=\frac{6}{10}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12}{2*5}=\frac{30}{10}
=3
$