y^2-10y=-4

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

y^2-10y=-4

We move all terms to the left:

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

We add all the numbers together, and all the variables

y^2-10y+4=0

a = 1; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·1·4
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{21}}{2*1}=\frac{10-2\sqrt{21}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{21}}{2*1}=\frac{10+2\sqrt{21}}{2}
$