y^2+9y2=8y+58

Solution for y^2+9y2=8y+58 equation:

y^2+9y^2=8y+58

We move all terms to the left:

y^2+9y^2-(8y+58)=0

We add all the numbers together, and all the variables

10y^2-(8y+58)=0

We get rid of parentheses

10y^2-8y-58=0

a = 10; b = -8; c = -58;
Δ = b2-4ac
Δ = -82-4·10·(-58)
Δ = 2384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2384}=\sqrt{16*149}=\sqrt{16}*\sqrt{149}=4\sqrt{149}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{149}}{2*10}=\frac{8-4\sqrt{149}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{149}}{2*10}=\frac{8+4\sqrt{149}}{20}
$