86-5y+9y^2=90

Solution for 86-5y+9y^2=90 equation:

86-5y+9y^2=90

We move all terms to the left:

86-5y+9y^2-(90)=0

We add all the numbers together, and all the variables

9y^2-5y-4=0

a = 9; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·9·(-4)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*9}=\frac{-8}{18}
=-4/9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*9}=\frac{18}{18}
=1
$