35=-0.05x^2+6x-100

Solution for 35=-0.05x^2+6x-100 equation:

35=-0.05x^2+6x-100

We move all terms to the left:

35-(-0.05x^2+6x-100)=0

We get rid of parentheses

0.05x^2-6x+100+35=0

We add all the numbers together, and all the variables

0.05x^2-6x+135=0

a = 0.05; b = -6; c = +135;
Δ = b2-4ac
Δ = -62-4·0.05·135
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-3}{2*0.05}=\frac{3}{0.1}
=30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+3}{2*0.05}=\frac{9}{0.1}
=90
$