y^2-30y+100=10

Solution for y^2-30y+100=10 equation:

y^2-30y+100=10

We move all terms to the left:

y^2-30y+100-(10)=0

We add all the numbers together, and all the variables

y^2-30y+90=0

a = 1; b = -30; c = +90;
Δ = b2-4ac
Δ = -302-4·1·90
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{15}}{2*1}=\frac{30-6\sqrt{15}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{15}}{2*1}=\frac{30+6\sqrt{15}}{2}
$