x=110x-3x^2

Solution for x=110x-3x^2 equation:

x=110x-3x^2

We move all terms to the left:

x-(110x-3x^2)=0

We get rid of parentheses

3x^2-110x+x=0

We add all the numbers together, and all the variables

3x^2-109x=0

a = 3; b = -109; c = 0;
Δ = b2-4ac
Δ = -1092-4·3·0
Δ = 11881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11881}=109$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109)-109}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109)+109}{2*3}=\frac{218}{6}
=36+1/3
$