4y-10=y^2-62

Solution for 4y-10=y^2-62 equation:

4y-10=y^2-62

We move all terms to the left:

4y-10-(y^2-62)=0

We get rid of parentheses

-y^2+4y+62-10=0

We add all the numbers together, and all the variables

-1y^2+4y+52=0

a = -1; b = 4; c = +52;
Δ = b2-4ac
Δ = 42-4·(-1)·52
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{14}}{2*-1}=\frac{-4-4\sqrt{14}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{14}}{2*-1}=\frac{-4+4\sqrt{14}}{-2}
$