y^2-62=2y-5

Solution for y^2-62=2y-5 equation:

y^2-62=2y-5

We move all terms to the left:

y^2-62-(2y-5)=0

We get rid of parentheses

y^2-2y+5-62=0

We add all the numbers together, and all the variables

y^2-2y-57=0

a = 1; b = -2; c = -57;
Δ = b2-4ac
Δ = -22-4·1·(-57)
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{58}}{2*1}=\frac{2-2\sqrt{58}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{58}}{2*1}=\frac{2+2\sqrt{58}}{2}
$