Y=1/1-5x+6x^2

Solution for Y=1/1-5x+6x^2 equation:

=1/1-5Y+6Y^2

We move all terms to the left:

-(1/1-5Y+6Y^2)=0


Domain of the equation: 1-5Y+6Y^2)!=0

We move all terms containing Y to the left, all other terms to the right

6Y^2)-5Y!=-1

Y∈R


We get rid of parentheses

-6Y^2+5Y-1/1=0

Fractions to decimals

-6Y^2+5Y+1=0

a = -6; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·(-6)·1
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*-6}=\frac{-12}{-12}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*-6}=\frac{2}{-12}
=-1/6
$